In this paper, a fractional order calculus based least mean square algorithm is proposed for complex system identification. The proposed algorithm, named as, fractional complex least mean square (FCLMS), successfully deals with the problem of complex error due to negative weights or complex input/output in the FLMS. For the evaluation purpose a complex linear system is considered. The FCLMS algorithm successfully identifies the complex system and achieve high convergence rate without compromising the steady state error. The convergence rate of the proposed FCLMS is two times better than that of the complex least mean square (CLMS).