Recently, the complex valued metric spaces which is more general than the metric spaces was introduced by Azam et al. (2011). They also established the existence of fixed point theorems under the contraction condition in this space. The aim of this paper is to extend and improve the condition of Azam et al.'s contraction to obtain the existence of fixed point theorems for complex valued metric spaces. The existence of a common fixed point theorem is applied to obtain the existence theorem for Urysohn's integral equation.