A joint sparse reconstruction method is proposed for the estimation of the direction-of-arrival (DOA) of narrowband or wideband signals by using a co-centered orthogonal loop and dipole (COLD) vector antenna array. This method is based on the sparse representation of the first column vector of the polarization-space covariance matrix constructed by the output of the COLD array, which can be regarded as two perpendicular loops and dipole separated antenna arrays. The DOA estimates are then obtained via the convex optimation (l1-norm based) joint sparse reconstruction technique under the l2-norm constraint. Simulation results show the superior performance of the presented method over the traditional methods in terms of resolution and DOA estimation accuracy.