Spiking Neural Networks (SNNs) contain more biologically realistic structures and biologically-inspired learning principles than those in standard Artificial Neural Networks (ANNs). SNNs are considered the third generation of ANNs, powerful on the robust computation with a low computational cost. The neurons in SNNs are non-differential, containing decayed historical states and generating event-based spikes after their states reaching the firing threshold. These dynamic characteristics of SNNs make it difficult to be directly trained with the standard backpropagation (BP), which is also considered not biologically plausible. In this paper, a Biologically-plausible Reward Propagation (BRP) algorithm is proposed and applied to the SNN architecture with both spiking-convolution (with both 1D and 2D convolutional kernels) and full-connection layers. Unlike the standard BP that propagates error signals from post to presynaptic neurons layer by layer, the BRP propagates target labels instead of errors directly from the output layer to all pre-hidden layers. This effort is more consistent with the top-down reward-guiding learning in cortical columns of the neocortex. Synaptic modifications with only local gradient differences are induced with pseudo-BP that might also be replaced with the Spike-Timing Dependent Plasticity (STDP). The performance of the proposed BRP-SNN is further verified on the spatial (including MNIST and Cifar-10) and temporal (including TIDigits and DvsGesture) tasks, where the SNN using BRP has reached a similar accuracy compared to other state-of-the-art BP-based SNNs and saved 50% more computational cost than ANNs. We think the introduction of biologically plausible learning rules to the training procedure of biologically realistic SNNs will give us more hints and inspirations toward a better understanding of the biological system's intelligent nature.