In the applications of deep-space exploration, surveillance, threat detection and high resolution investigation on the ground, space optical systems need not only both the high resolution and width of view zoom system, but also the small size, light weight, low power and fast focusing system. As the traditional mechanical zoom system requires complex and precision mechanical motion, many problems are usually caused. Thus, based on active optics, the active optical elements are applied to the imaging system, and it is proposed that the optical element curvature radius should be variable to realize the transition among the different focal lengths. According to third-order aberration theory and dimension calculation of optical system requirement, the active zoom theory is studied, and the third-order aberration equation constraints are confirmed. Then the initial construction parameters of coaxial active zoom system are achieved by solving the equations. The system is optimized with using the optical design software ZEMAX. The system consists of the static primary mirror, the secondary and third mirror with the variable curvature radius, and the plane mirror with zero-power. As two times the light is obscured by the elements in the coaxial active zoom system, the amount of the energy on the image plane will be affected. For this reason, it is proposed that the unobstructed off-axis optimization should be necessary to the coaxial system. The off-axis system design theory is studied and the off-axis active zoom system is designed.