Abstract: In this paper we deal with the optimal predicated problem for distributed parameter system-state of Gauss-Markov, which can be described by vector difference integral equations. When the optimal filtered estimate and covariance matrix are known the optimal preredicated formula and the covariance matrix equation of the system state are derived, moreover we have shown that the obtained predicated error process is also a Gauss-Markov distributed parameter process. We have shown that the optimal recursive filtered estimate formula and equations for error covariance can be derived by projection lemma.