Quasi-isentropic compression is an effective method to achieve high-density and high-temperature implosion in laser-driven inertial confinement fusion (ICF). However, it requires precise matching between the laser profile and the target structure. Designing the optimal laser profile and the corresponding target for ICF is a challenge due to the large number of parameters involved. In this paper, we present a novel method that combines random walk and Bayesian optimization. The basic sampling data for Bayesian optimization are a series of laser pulse profiles and target structures that can produce relatively high areal densities obtained by the random walk method. This approach reduces the number of samples required for Bayesian optimization and mitigates low efficiency in the latter stages of the random walk method. The method also reduces the randomness in the optimization process and enhances the optimization efficiency. It should have important applications in ICF research.