Average biodegradation rate of newly filled municipal solid waste (MSW) in landfills is relatively fast, and the landfill gas produced by the new MSW biodegradation can cause great variations in gas pressure. To predict the gas pressure distribution in the MSW layer, a one-dimensional gas transport model is established in this study. The following factors are considered in this model: (1) the variation of gas permeability with depth; (2) the anisotropy ratio of gas permeability; (3) the settlement caused by waste biodegradation. Furthermore, a single peak model for gas production is applied as the source term of gas production. The equation for settlement caused by waste biodegradation is presented, and the time of peak gas production rate is obtained by fitting the settlement of the newly filled layer. The stratification of the unsaturated and saturated regions is taken into account by distinguishing the difference in gas saturation. The layering of the new and old waste layers is considered by distinguishing the difference in the length of time that waste has been degraded to produce gas. Based on the method of numerical calculation, the gas pressure distribution in the landfill with layered new and old MSW is well simulated. The position where the maximum gas pressure occurs is found. The sensitivity analysis shows that the influence of the anisotropy ratio on gas pressure distribution is more significant.