Based on the macroeconomic ideas of Goodwin and Puu, this article derived a generalized nonlinear dynamical business cycle system.First, the numerical methods were used to investigate the global bifurcation behaviors of the system depending on certain parameters. Then, by means of the largest Lyapunov exponent, the variations of the dynamical characters during the bifurcation were discussed.Through the bifurcation figures,we found the perioddoubling bifurcation route to chaos within some parameter intervals,and there were several periodic windows embedded in the chaotic domains. Besides, the increase of “accelerator" value can improve the cyclical motion of economics. Finally, the potential applications of the dynamical properties by bifurcation and chaos analysis to understanding economic fluctuations were introduced.