The transmission loss of photons during quantum key distribution(QKD) process leads to the linear key rate bound for practical QKD systems without quantum repeaters. Phase matching quantum key distribution (PM-QKD) protocol, an novel QKD protocol, can overcome the constraint with a measurement-device-independent structure, while it still requires the light source to be ideal. This assumption is not guaranteed in practice, leading to practical secure issues. In this paper, we propose a modified PM-QKD protocol with a light source monitoring, named PM-QKD-LSM protocol, which can guarantee the security of the system under the non-ideal source condition. The results show that our proposed protocol performs almost the same as the ideal PM-QKD protocol even considering the imperfect factors in practical systems. PM-QKD-LSM protocol has a better performance with source fluctuation, and it is robust in symmetric or asymmetric cases.