It is well known that Kalman Filter is good for a state estimation on a linear system. The criterion is a square error function, which is efficient and sufficient for most systems. However, the square error evaluation function is often not sufficient in the systems under non-Gaussian noise. In recent years, an entropy has been attracting attention as an evaluation function changing to the square error criterion. Beginning with entropy of Shannon, its characteristics are related to higher-order statistics. When the entropy is set as criterion, all moments or all even moments of the state estimation error can be constrained. These characteristics have been utilized for learning system, adaptive filtering, and neuro-control. In this research, we focus on a correntropy, which has expanded Renyi 's entropy more generally, and the correntropy is utilized in order to estimate states of systems. This method uses multi-step ahead predictions, and aims to better state estimation. The method of multi-step ahead predictions is effective for the case that the system has not only statistic process noise but also other disturbances. Previous methods using the correntropy as a criterion are introduced here, and compared with modified method through experimental data.