I got married before 1 and half year , bt since last one year I am staying separate from my husband can I claim alimony? Or divorce is compulsory for claiming alimony?

Alimony is only part of a divorce settlement, if so ordered by the divorce court or agreed on mutually before filing for a no fault divorce.
What country are you in, or from, in the US (since it sounds like you might not be American?)

i got married before 1 and half year , bt since last one year I am staying separate from my husband can i claim alimony ?? or divorce is compulsory for claiming alimony??

In many places there is provision for a separation. A separation agreement could well provide for spousal support.

But if you can't reach an agreement, usually court ordered spousal support is not in the cards, unless there is a divorce.