The phase-matching quantum key distribution (PM-QKD), one of the variants of Twin-Field (TF) QKD protocol, was recently proposed to overcome the rate-distance limits of point to point protocol without quantum repeaters. In this paper, we propose a more practical PM-QKD protocol version with four-intensity decoy states and source errors, since neither the infinite decoy states nor the precise control of the light source is available in practice. We present the formulation of the secure key rate of the proposed protocol and analyze the performances of the protocol with and without source errors by numerical simulations.