Spiking neural networks (SNNs) are more energy- and resource-efficient than artificial neural networks (ANNs). However, supervised SNN learning is a challenging task due to non-differentiability of spikes and computation of complex terms. Moreover, the design of SNN learning engines is not an easy task due to limited hardware resources and tight energy constraints. In this article, a novel hardware-efficient SNN back-propagation scheme that offers fast convergence is proposed. The learning scheme does not require any complex operation such as error normalization and weight-threshold balancing, and can achieve an accuracy of around 97.5% on MNIST dataset using only 158,800 synapses. The multiplier-less inference engine trained using the proposed hard sigmoid SNN training (HaSiST) scheme can operate at a frequency of 135 MHz and consumes only 1.03 slice registers per synapse, 2.8 slice look-up tables, and can infer about 0.03× 10 features in a second, equivalent to 9.44 giga synaptic operations per second (GSOPS). The article also presents a high-speed, cost-efficient SNN training engine that consumes only 2.63 slice registers per synapse, 37.84 slice look-up tables per synapse, and can operate at a maximum computational frequency of around 50 MHz on a Virtex 6 FPGA.