Is it still possible to get a green card if I divorce one year after marrying U.S. citizen

From your question, I understand you are married to a US citizen and you want to get a divorce because of his alcoholism.

It may be possible for you to qualify for some kind of relief. You would want to consult with an immigration attorney in your local area to see what options you have. One thing you would want to explore with an immigration attorney is the Violence Against Women Act (VAWA), which is discussed at length at www.uscis.gov. (Except here):

How Do I Apply for Immigration Benefits as a Battered Spouse or Child?

Background
Generally, U.S. citizens (USC) and Lawful Permanent Residents (LPRs) file an immigrant visa petition with the U.S. Citizenship and Immigration Services (USCIS) on behalf of a spouse or child, so that these family members may emigrate to or remain in the United States. USCIS Form I-130, Petition for Alien Relative is filed by the USC/LPR, the petitioner, on behalf of the family member who is the beneficiary. The petitioner controls when or if the petition is filed. Unfortunately, some U.S. citizens and LPRs misuse their control of this process to abuse their family members, or by threatening to report them to the USCIS. As a result, most battered immigrants are afraid to report the abuse to the police or other authorities.

Under the Violence Against Women Act (VAWA) passed by Congress in 1994, the spouses and children of United States citizens or lawful permanent residents (LPR) may self-petition to obtain lawful permanent residency. The immigration provisions of VAWA allow certain battered immigrants to file for immigration relief without the abuser's assistance or knowledge, in order to seek safety and independence from the abuser. Victims of domestic violence should know that help is available to them through the National Domestic Violence Hotline on 1-800-799-7233 or 1-800-787-3224 [TDD] for information about shelters, mental health care, legal advice and other types of assistance, including information about self-petitioning for immigration status.

What is the Legal Foundation?
The Immigration and Nationality Act (INA) is the law that governs immigration in the United States. The Violence Against Women Act (VAWA) provisions relating to immigration are codified in section 204(a) of the INA. Rules published in the Federal Register explain the eligibility requirements and procedures for filing a self-petition under the VAWA provisions. These rules can be found in the Code of Federal Regulations at 8 CFR § 204. The Battered Immigrant Women Protection Act of 2000 (BIWPA) made significant amendments to section 204(a) of the INA. Self-petitions may be filed according to the amended requirements but adjudication may be delayed until rules are published.

Who is Eligible?
To be eligible to file a self-petition (an application that you file for yourself for immigration benefits) you must qualify under one of the following categories:

Spouse: You may self-petition if you are a battered spouse married to a U.S. citizen or lawful permanent resident. Unmarried children under the age of 21, who have not filed their own self-petition, may be included on your petition as derivative beneficiaries.

Parent: You may self-petition if you are the parent of a child who has been abused by your U.S. citizen or lawful permanent resident spouse. Your children (under 21 years of age and unmarried), including those who may not have been abused, may be included on your petition as derivative beneficiaries, if they have not filed their own self-petition.

Child: You may self-petition if you are a battered child (under 21 years of age and unmarried) who has been abused by your U.S. citizen or lawful permanent resident parent. For more information, please see How Do I Bring My Child to Live in the United States?. Your children (under 21 years of age and unmarried), including those who may not have been abused, may be included on your petition as derivative beneficiaries