The ability to adapt behavior to maximize reward as a result of interactions with the environment is crucial for the survival of any higher organism. In the framework of reinforcement learning, temporal-difference learning algorithms provide an effective strategy for such goal-directed adaptation, but it is unclear to what extent these algorithms are compatible with neural computation. In this article, we present a spiking neural network model that implements actor-critic temporal-difference learning by combining local plasticity rules with a global reward signal. The network is capable of solving a nontrivial gridworld task with sparse rewards. We derive a quantitative mapping of plasticity parameters and synaptic weights to the corresponding variables in the standard algorithmic formulation and demonstrate that the network learns with a similar speed to its discrete time counterpart and attains the same equilibrium performance.