Physical Review Letters 101, 250602 (2008) We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the {\em projected entangled-pair state} algorithm for finite lattice systems F. Verstraete and J.I. Cirac, cond-mat/0407066 and the infinite {\em time-evolving block decimation} algorithm for infinite one-dimensional lattice systems G. Vidal, Phys. Rev. Lett. 98, 070201 (2007). The present algorithm allows for the computation of the ground state and the simulation of time evolution in infinite two-dimensional systems that are invariant under translations. We demonstrate its performance by obtaining the ground state of the quantum Ising model and analysing its second order quantum phase transition.