A finite time convergent guidance law based on variable universe fuzzy adaptive sliding mode was proposed for intercepting high speed and maneuvering targets. Firstly, the missile-target interception model was derived and the three-dimensional sliding mode guidance law was designed. Secondly, according to the expert experience of finite time convergent guidance laws, the fuzzy adaptive control method was adopted to approximate the consecutive items of the sliding mode guidance law, and the finite time convergent control rules were designed. Finally, a new expansion factor for variable universe was proposed and the variable universe fuzzy adaptive sliding mode guidance law with finite time convergence based on new expansion factor was proposed. Simulation results show that the proposed guidance law can hit the target correctly and achieve the finite time convergence ability of the line-of-sight. Besides, compared with the proportional navigation guidance law, the proposed guidance law has better guidance precision and shorter flight time.