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In this paper, a novel dynamic system, the fractional-order complex Chen system, is presented for the first time. Dynamic behaviors of system are studied analytically and numerically. Different routes to chaos are shown, and diverse kinds of motions are identified and exhibited by means of bifurcation diagram, portrait phase and the largest Lyapunov exponent. Secondly, an application to digital secure communication based on the novel system is proposed, in which security is enhanced by continually switching different orders of derivative in an irregular pattern. Furthermore, making full use of the advantage of high-capacity transmission of complex system, the improved digital secure communication scheme is achieved based on hybrid synchronization in coupled fractional-order complex Chen system, that means anti-synchronization in real part of state variables and projective synchronization in imaginary part, respectively. The corresponding numerical simulations demonstrate the effectiveness and feasibility of the proposed schemes.