This paper presents a majorization-minimization-based framework for learning time-varying graphs from spatial-temporal measurements with non-convex penalties. The proposed approach infers time-varying graphs by using the log-likelihood function in conjunction with two non-convex regularizers. Using the log-likelihood function under a total positivity constraint, we can construct the Laplacian matrix from the off-diagonal elements of the precision matrix. Furthermore, we employ non-convex regularizer functions to constrain the changes in graph topology and associated weight evolution to be sparse. The experimental results demonstrate that our proposed method outperforms the state-of-the-art methods in sparse and non-sparse situations.