In this paper, a fracture mechanics model that deals with fracture growth in layered low-permeability rocks is presented and applied to hydraulic fracturing stimulation of coal seam gas reservoirs. The model uses the conventional pseudo-3D treatment by which the vertically planar fracture is divided into cells along the horizontal direction. For each cell, the fracture deformation is represented by a 2D plane-strain fracture. To ensure numerical stability, the model uses an optimization method based on the fluid volume increase of each cell and the solutions for each cell can be obtained in parallel when using a computer with multiple CPU cores. The method was verified based on the comparisons with existing solutions and the computational speed can be significantly increased by using parallel computing. Numerical examples are presented to illustrate cases that result in fracture geometrical complexities caused by material properties contrasts between the thin softer coal seams and the adjacent stiffer rocks. The local horizontal stresses in each layer are calculated based on the layer-independent uniform horizontal strain assumption. The overburden stress is given. The fracture length and opening in the coal can be larger than other layers if the coal is subject to a smaller stress. This will promote growth of the fracture plane to include coal seams that do not receive injected fluid at the wellbore. The well developed fracture opening in the coal can be impeded by an increase in the confining stress of the coal. The fracturing produces wide propped channels below the coal seam in the low stress rock that exists there. These conductive channels allow flow of gas and water to the wellbore. The stress uncertainty is considered and interestingly the injection pressure trends are insensitive to the variation of local stresses. There is a process that favors growth in the softer coal seams for all cases, which yields a slight and progressive increase in the injection pressure.