Time-parallel simulation offers the potential of massive parallelization of a simulation application, due to the amount of achievable parallelism not being restricted by the decomposability of the state space of a simulation model. Unfortunately, the potential speedup of a time-parallel simulation highly depends on the ability to match final and initial states of adjacent time intervals. Depending on the properties of the underlying simulation model, it might be feasible to accept a simulation iteration, even if the states of adjacent time intervals do not match exactly. This leads to the concept of approximative state matching in time-parallel simulation, which is introduced in this paper. Experiments with a prototypical implementation of a simple simulation model show encouraging results in terms of simulation speedup and introduced error.