In sound source direction of arrival (DOA) estimation, one of the typical methods is based on the time difference of arrival (TDOA). For the TDOA-based sound source DOA estimation, the TDOA-DOA mapping is a crucial step. Here, we propose a TDOA-DOA mapping approach based on the multi-kernel least-squares support vector regression (LS-SVR), and also analyze its performance with sparsification. In addition, we present an outlier detection method based on the normalized median filtering to post-process the TDOA estimation for improving the performance of TDOA-DOA mapping in noisy reverberant environments. Simulation results show that the proposed method is superior to its counterparts, such as LS and single-kernel LS-SVR methods.