An approximate solution is presented for the spherical diffusion equation for the spherical particles in a physics-based lithium-ion battery model. This approximate solution is compared to different numerical and analytic solutions for various boundary conditions. These comparisons reveal that our approximate solution can provide accuracy and time-efficiency in simulation. This approximate solution is much faster than the numerical and truncated analytical solutions at high current rate, and shows better long-time accuracy than the short-time analytical solution. This approximate solution can also be used as the porous electrode model.