Summary: The objective of this paper is to develop a robust Maximum Likelihood Estimation (MLE) for the stochastic state space model via the expectation maximization algorithm to cope with observation outliers. Two types of outliers and their influence are studied in this paper: namely, the Additive Outlier (AO) and Innovative Outlier (IO). Due to the sensitivity of the MLE to AO and IO, we propose two techniques for robustifying the MLE: the Weighted Maximum Likelihood Estimation (WMLE) and the Trimmed Maximum Likelihood Estimation (TMLE). The WMLE is easy to implement with weights estimated from the data; however, it is still sensitive to IO and a patch of AO outliers. On the other hand, the TMLE is reduced to a combinatorial optimization problem and hard to implement but it is efficient to both types of outliers presented here. To overcome the difficulty, we apply the parallel randomized algorithm that has a low computational cost. A Monte Carlo simulation result shows the efficiency of the proposed algorithms.