During blasting, rock failure is caused by blasting wave and explosive gas pressure, as a multi-field coupled process. Most numerical models focus on the effect of blasting wave where the gas pressure is commonly accounted for by empirical relations, ignoring the penetration and permeation of gas flow in cracks. This can underestimate the failure region. In this work, a novel multi-field model is developed in the framework of a continuous-discontinuous element method (CDEM), which is a coupled finite-discrete method with explicit integration strategy. The deformation and cracking of rock mass and the distribution of gas pressure are captured. The proposed method is verified by comparing the results to other results provided in published literature. Especially, by simulating the cases with blocked and unblocked blasting hole, we found that: (i) The fracture degree of the case with blocked blasting hole was 30% higher than that of the unblocked blasting hole. (ii) The radial main cracks in the fracture area are mainly caused by the explosive gas, and the tiny and dense cracks near the hole are induced by the explosion stress wave. (iii) The explosion crushing zone is mainly formed by the action of explosion stress wave, while the crack zone is formed by the combined action of the explosion stress wave and explosive gas. The proposed method provides a useful tool to properly simulate a rock blasting process.