In this paper, we firstly study numerical methods for gas flow simulation in dual-continuum porous media. Typical methods for oil flow simulation in dual-continuum porous media cannot be used straightforward to this kind of simulation due to the artificial mass loss caused by the compressibility and the non-robustness caused by the non-linear source term. To avoid these two problems, corrected numerical methods are proposed using mass balance equations and local linearization of the non-linear source term. The improved numerical methods are successful for the computation of gas flow in the double-porosity double-permeability porous media. After this improvement, temporal advancement for each time step includes three fractional steps: (i) advance matrix pressure and fracture pressure using the typical computation; (ii) solve the mass balance equation system for mean pressures; (iii) correct pressures in (i) by mean pressures in (ii). Numerical results show that mass conservation of gas for the whole domain is guaranteed while the numerical computation is robust.