Optical Kerr solitons generation based on microresonators is essential in nonlinear optics. Among various soliton generation processes, the single soliton generation plays a pivotal role since it ensures rigorous mode-locking on each comb line whose interval equals the free spectral range (FSR) of the microresonator. Current studies show that single soliton generation is challenging due to cavity instability. Here, we propose a new method to greatly improve single soliton generation probalility in the anomalous group velocity dispersion (GVD) regime in a micro-ring resonator based on silicon nitride. The improvement is realized by introducing mode depletion through an integrated coupled filter. It is convenient to introduce controllable single mode depletion in a micro-ring resonator by adjusting the response function of a coupled filter. We show that spectral mode depletion (SMD) can significantly boost the single soliton generation probability. The effect of SMD on the dynamics of optical Kerr solitons generation are also discussed. The proposed method offers a straightforward and simple way to facilitate robust single soliton generation, and will have an impact on the research development in optical Kerr soliton generation and on-chip optical frequency mode manipulation.