In this paper, we investigate Mira 2 map in parameter-space (A-B) and obtain some interesting dynamical behaviors. According to the parameter space of Mira 2 map, we take A and B as some groups of values and display complex dynamical behaviors, including period-1, 2, 3, 4, 5, ???, 38, ??? orbits, Arnold tongues observed in the circle map [7], crisis, some chaotic attractors, period-doubling bifurcation to chaos, quasi-period behaviors to chaos, chaos to quasi-period behaviors, bubble and onset of chaos.