en تخصصي Special پژوهشي Research In this paper we consider a constrained optimization problem where the objectives are fuzzy functions (fuzzy-valued functions). Fuzzy constrained Optimization (FO) problem plays an important role in many fields, including mathematics, engineering, statistics and so on. In the other side, in the real situations, it is important to know how may obtain its numerical solution of a given interesting problem. In this paper we defined Necessary and sufficient optimality conditions for constrained fuzzy optimization problem and a Hybrid Conjugate Gradient (HCG) algorithm was proposed for solving FOP. The parametric form of the function was translated into an equivalent Fuzzy constrained Optimization (FO) problem. Then, HCG algorithm was applied to solve the corresponding optimization problem.<br> &nbsp; Fuzzy constrained Optimization, Hybrid Conjugate Gradient Algorithm, constrained Optimization Problem, Steepest Descent Algorithm, Generalized Hukuhara differentiability 47 52 http://ijorlu.lahijan.iau.ir/browse.php?a_code=A-10-473-1&slc_lang=en&sid=1 M. Ranjbar 10031947532846001056 10031947532846001056 Yes Department of Mathematics, University of Mazandaran, Babolsar, Iran Z. Akbari 10031947532846001057 10031947532846001057 No Department of Mathematics, University of Mazandaran, Babolsar, Iran