A complex network design method that finds a desired network structure can become one of strong tools in large-scale system designs. Conventional complex network design methods only tackle static networks, that is, they do not consider the growth of a target network. In this study, we propose a new growing complex network design method. First, let us consider evalution functions which quantitatively express characteristics of desired stuructures using feature quantities. Then, we formulate a growing complex network design problem as a multi-objective optimization problem in order to determine connection targets of a new node using the evaluation functions. Solving the problem, we grow the network, then, we obtain a desired network. We try to generate networks which have desired clustering coefficient and average path concurrently. Through numerical experiments, we confirmed the proposed method is effective as a growing complex network design method.