Transmission delays are an inherent component of spiking neural networks (SNNs) but relatively little is known about how delays are adapted in biological systems and studies on computational learning mechanisms have focused on spike-timing-dependent plasticity (STDP) which adjusts synaptic weights rather than synaptic delays. We propose a novel algorithm for learning temporal delays in SNNs with Gaussian synapses, which we call spike-delay-variance learning (SDVL). A key feature of the algorithm is adaptation of the shape (mean and variance) of the postsynaptic release profiles only, rather than the conventional STDP approach of adapting the network's synaptic weights. The algorithm's ability to learn temporal input sequences was tested in three studies using supervised and unsupervised learning within feed-forward networks. SDVL was able to successfully classify forty spatiotemporal patterns without supervision by providing robust, effective adaption of the postsynaptic release profiles. The results demonstrate how delay learning can contribute to the stability of spiking sequences, and that there is a potential role for adaption of variance as well as mean values in learning algorithms for spiking neural networks.