The problem of interference alignment in time-varying MIMO interference channels is considered. To reduce complexity, an adaptive algorithm for beam vector design is proposed based on our previous work of least squares approach to beam design for interference alignment and matrix perturbation theory. The proposed algorithm calculates interference-aligning beam vectors by additive update of the previous value and reduces complexity signi cantly. Numerical results are provided to validate the proposed algorithm. It is shown that the proposed adaptive algorithm yields almost the same performance as a non-adaptive method that calculates interferencealigning beam vectors at every time step.