A typical quantum state obeying the area law for entanglement on an infinite two-dimensional (2D) lattice can be represented by a tensor network Ansatz, known as an infinite projected entangled pair state (iPEPS), with a finite bond dimension D . Its real-imaginary time evolution can be split into small time steps. An application of a time step generates a new iPEPS with a bond dimension k times the original one. The new iPEPS does not make optimal use of its enlarged bond dimension k D ; hence, in principle, it can be represented accurately by a more compact Ansatz, preferably with the original D . In this work we show how the more compact iPEPS can be optimized variationally to maximize its overlap with the new iPEPS. To compute the overlap we use the corner-transfer-matrix renormalization group. By simulating sudden quench of the transverse field in the 2D quantum Ising model with the proposed algorithm, we provide a proof of principle that real-time evolution can be simulated with iPEPS. A similar proof is provided with the same model for imaginary-time evolution of purification of its thermal states.