This paper presents a mesoscale phase-field fracture model formulation for simulating the fracture process of concrete at the mesoscale, focusing on studying size effects on the formation and evolution of the fracture process zone (FPZ). The proposed model is firstly verified and validated for concrete structures subjected to uniaxial tension tests. The model is further extended for modelling the formation and evolution of the FPZ in a concrete notched beam under three-point bending tests. Results demonstrate that the proposed model can not only capture the macro response in terms of the load–displacement curve but also can realistically depict the complex fracture process inside concrete under tension-dominated loading. The effects of specimen size on the evolution of the FPZ are also investigated with the proposed model. Based on the simulation results, it may be concluded that while the width of the FPZ is insensitive to the beam size and therefore can be considered to be a material constant, the length of the FPZ is generally strongly dependent on the specimen size. This characteristic of the FPZ in concrete has beneficial implications for understanding the overall size effect phenomenon.