In this paper, we present an output error identification algorithm for multi-input/multi-output (MIMO) switched linear systems with bounded noise on the output. To our knowledge, no identification algorithm has been proposed for the identification of MIMO-Switched Output Error (MIMO-SOE) model. This problem includes the estimation of the discrete state that indicates the active sub-model at each time and the estimation of the parameters vectors of all sub-models. The proposed algorithm is an adapted Outer Bounding Ellipsoid (OBE) type algorithm suitable for system identification with bounded noise. We show by a numerical example that our algorithm performs well and provides good performance with low computational complexity.