Using the homotopy analysis method (HAM), the nonlinear equation of the jamming transition problem (JTP) in traffic flow is discussed, which is based on the Lorentz system. Through choosing different initial approximation solutions and different linear operators, approximation solutions of the JTP and the corresponding residual errors are obtained respectively. By comparing the present results with the previous related studies, the following conclusions can be drawn that the HAM is superior to the differential transform method; however, a linear operator should be chosen as best you can to approach the linear part of the original operator in using the HAM. A new method to choose the initial approximation solution (named double HAM) is given. The correctness of the theoretical analysis is verified by numerical simulation.