When we use an adaptive array antenna (AAA) with the minimum mean square error (MMSE) criterion under the multipath environment, where the receiving signal level varies, it is difficult for the AAA to converge because of the distortion of the desired wave. Then, we need the equalization both in space and time domains. A tapped-delay-line adaptive array antenna (TDL-AAA) and the AAA with linear equalizer (AAA-LE) have been proposed as simple space-temporal equalization. The AAA-LE has not utilized the recursive least square (RLS) algorithm. In this paper, we propose a space-temporal simultaneous processing equalizer (ST-SPE) that is an AAA-LE with the RLS algorithm. We proposed that the first tap weight of the LE should be fixed and the necessity of that is derived from a normal equation in the MMSE criterion. We achieved the space-temporal simultaneous equalization with the RLS algorithm by this configuration. The ST-SPE can reduce the computational complexity of the space-temporal joint equalization in comparison to the TDL-AAA, when the ST-SPE has almost the same performance as the TDL-AAA in multipath environment with minimum phase condition such as appeared at line-of-sight (LOS).