Passive bistatic radar detects targets by exploiting available local broadcasters and communication transmissions as illuminators, which are not designed for radar. The signal usually contains a time-varying structure, which may result in high-level range ambiguity sidelobes. Because the mismatched filter is effective in suppressing sidelobes, it can be used in a passive bistatic radar. However, due to the low signal-to-noise ratio in the reference signal, the sidelobe suppression performance seriously de-grades in a passive bistatic radar system. To solve this problem, a novel mismatched filtering algorithm is developed using worst-case performance optimization. In this algorithm, the influence of the low energy level in the reference signal is taken into consideration, and a new cost function is built based on worst-case performance optimization. With this optimization, the mis-matched filter weights can be obtained by minimizing the total energy of the ambiguity range sidelobes. Quantitative evaluations and simulation results demonstrate that the proposed algorithm can realize sidelobe suppression when there is a low-energy ref-erence signal. Its effectiveness is proved using real data.