Can I loose my alimony from my ex husband if I move in with my boyfriend?

It largely depends on the terms of your divorce decree or settlement, as well as on the specific facts (e.g. how much does your boyfriend make? how much of the living expenses will he be paying? what are your responsibilities for your own expenses? etc.). Often, the decree or settlement will specify when and under what circumstances your alimony may cease; when those circumstances are set out clearly and plainly, those terms will be enforced.
If the decree or settlement does not address this situation, it is common, but not required, for alimony to cease when someone receiving it cohabitates with another. If your decree or agreement does not specify what happens, your ex can make a motion (a legal application to the court) and ask that your cohabitation be considered the equivalent of remarriage, which would end alimony. The court will then review the situation and decide if your new domestic arrangements are similar enough to remarriage as to justify terminating alimony. The law doesn't allow you to be married in all but name while still forcing your ex to pay alimony; on the other hand, if you are living with another and still fully responsible for all your own costs and/or you are supporting him, the court does not have to end your alimony (unless, that is, the terms of your divorce decree or settlement require that alimony end under these circumstances).