As an extension of traditional modal logics, this paper proposes a fuzzy first-order modal logic based on beilievable degree, and gives out a description of the fuzzy first-order modal logic based on constant domain semantics. In order to make the reasoning procedure between the fuzzy assertions efficiently, the notion of the fuzzy constraint is considered. A fuzzy constraint is an expression in which both syntax ingredient and semantics information are contained. By using the notion of the constraint, the reasoning procedure between the fuzzy assertions can be directly considered in the semantics environment, thus a fuzzy reasoning formal system which contains fuzzy constraint as its basic element is developed. As a main work of the paper, the relationship between the validity of the new assertion and the satisfiability of the fuzzy constraints is analyzed, and reasoning rules of the fuzzy reasoning formal system based on first order modal logic are given out. Further work could be done by considering the soundness and completeness of the formal system, and by building an efficient mechanism of reasoning procedure. The results have potential application in the areas of artificial intelligence and computer science.