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In this paper, a new iterative method for solving initial problem for linear and nonlinear partial differential equations is presented. Convergence analysis of iterative process is included. The proposed iterative scheme does not require any discretization, linearization or small perturbation and, compared to e.g. Adomian decomposition method or homotopy perturbation method, there is no need for calculation of generally n-dimensional integrals or derivatives, respectivelly. The approximate solution is calculated in the form of a sequence with easily computable terms. Depending on the form of the sequence it is possible to identify exact solution. Illustrative example is presented to demonstrate reliability and performance of the presented method. [ABSTRACT FROM AUTHOR]