For beyond fifth-generation and sixth-generation communication, intelligent reflecting surface (IRS)/reconfigurable intelligent surface, and cell-free networks have been proposed as revolutionary technologies, which could significantly improve the connection quality and coverage to meet future communication demands for extremely massive connectivity and high reliability. In this article, a transmit/passive beamforming strategy for multi-IRS assisted cell-free multi-input-multi-output network is proposed to maximize the weighted sum-rate (WSR). Specifically, for passive beamforming of IRS, an elementwise block coordinate descent framework is applied to efficiently solve the unit-modulus constraints and reduce computation complexity greatly. Note that, every variable in our proposed algorithm can be updated with closed-form solutions and our algorithm can be applied with distributed implementation. Both analytical and simulation results demonstrate that, while guaranteeing superiority in WSR performance and information interaction cost, the proposed scheme outperforms the benchmark algorithms with closed-form solutions significantly in terms of complexity cost.