It has been considered that an amount of calcium elevation in a synaptic spine determines whether the synapse is potentiated or depressed. However, it has been pointed out that simple application of the principle can not reproduce properties of spike-timing-dependent plasticity (STDP). To solve the problem, we present a possible mechanism using dynamically sliding threshold determined as the linear summation of calcium elevations induced by single pre- and post-synaptic spikes. We demonstrate that the model can reproduce the timing dependence of biological STDP. In addition, we find that the model can reproduce the dependence of biological STDP on the initial synaptic strength, which is found to be asymmetric for synaptic potentiation and depression, whereas no explicit initial-strength dependence nor asymmetric mechanism are incorporated into the model.