Object lookup is a basic problem in P2P network. Long-distance connections have been used to construct a searchable P2P network according to the small-world paradigm. Long-distance connections based on distance can achieve a searchable P2P network in theorem. However, it is hard to measure the lattice distance between two peers in real P2P network. On the other hand, it is easy to construct randomly selected long-distance connections with low overhead. We increase the number of randomly selected long-distance connections k to improve the performance of object lookup. Simulation results show there is some relation among k, the network size N and the average path length. The lower bound of k to achieve a searchable P2P network is still an open question.