Kuwait - Marriage

It is always possible to get married at the consulate or embassy of your home country if you wish to be married according to the law you are familiar with.

Local marriage

There is no legal impediment for a muslim and a non-muslim couple to get married under Shari’a or Islamic law.
The Muslim code applies to marriages wherein both parties are Muslims or wherein only the male party is a Muslim and the marriage is solemnized in accordance with the Muslim law (Article 13 PD 1083).

In fact, Prophet Mohammad, upon whom be peace, also married a non-Muslim woman by the name of Maria Kobti (Maria, the Copt), who later converted to Islam. Therefore, it is legal and valid to celebrate a marriage under Muslim law between a Muslim men and a non-Muslim woman.
Under Islamic law, a man may have up to four wives.

However, if you come from a different faith you are going to encounter some superable difficulties with the officiating Imam (Muslim priest), once he learned that the bride is not a Muslim, as Imam in practice only solemnizes marriage wherein both parties are Muslims.

Another possibility is to convert to the islamic faith, which is a request a woman might be asked to fullfill. In fact one of the concerns of a Muslim would be to ensure that future children are bred and nurtured under the care of a Muslim mother.

Prior proceeding ask yourself if you can, according to  your moral and social standing, accept to be married to a man, who could also be married to another woman.

It is in the broader interest of the family that before considering a marriage to ponder also to the consequences of the marriage based on its social and legal impact.