Functionally graded materials are regarded as a special kind of composites capable of eliminating material interfaces and the delamination problems. Stress discontinuity can be avoided owing to smooth composition of the functionally graded ingredients. In this study, a recently emerged effective non-local continuum theory for solving fracture problems in solids and structures, peridynamics, is employed to simulate dynamic wave propagation as well as crack propagation in functionally graded materials. Specifically, the ordinary state-based formulation is adopted. The ordinary state-based formulation is slightly modified for the modelling of functionally graded materials. The averaging technique is employed to determine peridynamic parameters associated with the material properties. Firstly, a benchmark problem is considered to validate the present implementation of ordinary state-based peridynamics for brittle fracture of homogeneous materials. Then, the wave propagation in the functionally graded materials under impact loading is simulated. Finally, dynamic crack propagation in the functionally graded materials is studied. The evaluated crack paths and the displacement waves are compared with reference works including numerical and experimental results. Good agreement between the reference and present results is achieved. It is shown that a simple modification of ordinary state-based formulation has led to simulate dynamic fracture of functionally graded materials.