Intelligent reflecting surface (IRS) is envisioned as a promising solution for controlling radio propagation environments in future wireless systems. In this paper, we propose a distributed intelligent reflecting surface (IRS) assisted multi-user millimeter wave (mmWave) system, where IRSs are exploited to enhance the mmWave signal coverage when direct links between base station and users are unavailable. First, a joint active and passive beamforming problem is established for weighted sum-rate maximization. Then, an alternating iterative algorithm with closed-form expressions is proposed to tackle the challenging non-convex problem, thereby decoupling the active and passive beamforming variables. Moreover, we design a constraint relaxation technique to address the unit modulus constraints pertaining to the IRS. Numerical results demonstrate that the distributed IRS can potentially enhance the communication performance of existing wireless systems.