We propose a novel l1l2-norm inverse solver for estimating the sources of EEG/MEG signals. Based on the standard l1-norm inverse solver, the proposed sparse distributed inverse solver integrates the l1-norm spatial model with a temporal model of the source signals in order to avoid unstable activation patterns and "spiky" reconstructed signals often produced by the original solvers. The joint spatio-temporal model leads to a cost function with an l1l2-norm regularizer whose minimization can be reduced to a convex second-order cone programming problem and efficiently solved using the interior-point method. Validation with simulated and real MEG data shows that the proposed solver yields source time course estimates qualitatively similar to those obtained through dipole fitting, but without the need to specify the number of dipole sources in advance. Furthermore, the l1l2-norm solver achieves fewer false positives and a better representation of the source locations than the conventional l2 minimum-norm estimates.