The accelerating expansion was discovered at the end of the last century, which violates humans′ fundamental intuition of gravity. Trying to explaining this weird observational fact became the principal task of cosmologists, who proposed various models. Among these models, gauge theories of gravity , for its solid theoretical foundation, attract widespread attention. In this paper, we study the cosmology based on the Poincaré gauge theory of gravity. We obtain the analytical solution which describes the evolution history of the universe. And we fit these analytical results to the Type Ia Supernova observation data, and obtain the best-fit value for model parameters and initial conditions, and the confidence level of these parameters.