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Nonlinear dynamics of a 1550-nm vertical-cavity surface-emitting laser with positive optoelectronic feedback are studied both numerically and experimentally. A mapping of dynamical states is presented in the parameter space of feedback delay time and feedback strength, where different states are identified and shown. A bifurcation diagram of the extrema of output peak series versus the feedback delay time is plotted. Various nonlinear dynamical behaviors, including regular pulsing, quasi-periodic pulsing, and chaotic pulsing, have been numerically and experimentally observed. Both numerical simulation and experimental observation indicate that the laser enters a chaotic pulsing state at certain delay times of the feedback loop through a quasi-periodic route.