Magnetic reconnection is a process that can rapidly convert magnetic field energy into plasma thermal energy and kinetic energy, and it is also an important energy conversion mechanism in space physics, astrophysics and plasma physics. Research related to analytical solutions for time-dependent three-dimensional magnetic reconnection is extremely difficult. For decades, several mathematical descriptions have been developed regarding different reconnection mechanisms, in which the equations based on magnetohydrodynamics theory outside the reconnection diffusion region are widely accepted. However, the equation set cannot be analytically solved unless specified constraints are imposed or the equations are reduced. Based on previous analytical methods for kinematic stationary reconnection, here the analytical solutions for time-dependent kinematic three-dimensional magnetic reconnection are discussed. In contrast to the counter-rotating plasma flows that existed in steady-state reconnection, it is found that spiral plasma flows, which have never been reported before, can be generated if the magnetic field changes exponentially with time. These analyses reveal new scenarios for time-dependent kinematic three-dimensional magnetic reconnection, and the deduced analytical solutions could improve our understanding of the dynamics involved in reconnection processes, as well as the interactions between the magnetic field and plasma flows during magnetic reconnection.