In this paper, optimal content caching strategy is proposed to jointly minimize the cell average outage probability and fronthaul usage in cloud radio access network (Cloud-RAN). At first, an accurate closed form expression of the outage probability conditioned on the user's location is presented, and the cell average outage probability is obtained through the composite Simpson's integration. The caching strategy for jointly optimizing the cell average outage probability and fronthaul usage is then formulated as a weighted sum minimization problem, which is a nonlinear 0-1 integer NP-hard problem. In order to deal with the NP-hard problem, two heuristic algorithms are proposed in this paper. Firstly, a genetic algorithm (GA) based approach is proposed. Numerical results show that the performance of the proposed GA-based approach with significantly reduced computational complexity is close to the optimal performance achieved by exhaustive search based caching strategy. Secondly, in order to further reduce the computational complexity, a mode selection approach is proposed. Numerical results show that this approach can achieve near-optimal performance over a wide range of the weighting factors through a single computation.