The development of memristor-based spiking neuromorphic systems (NS) has been essentially driven by the hope to replicate the extremely high energy efficiency of biological systems. Spike-timing-dependent plasticity (STDP) mechanism is considered as one of the most promising learning rules for NS. STDP learning has been observed in different types of biological synapses in presence of neuromodulators, e.g. dopamine, and is believed to be an enabling phenomenon for important biological functions such as associative and reinforcement learning. However, the direct STDP window change under dopamine-like modulation has not been yet demonstrated in memristive synapses. In this study, we experimentally demonstrate a simple way for the STDP window shape modulation by introducing the coefficients controlling the neuron spike amplitudes. In such a way the STDP window shape could be modulated from a classical asymmetric shape to a bell-shaped, as well as to anti-STDP and to anti-bell-shaped. The experiments have been carried out with (Co_0.4Fe_0.4B_0.2)_x(LiNbO₃)_1-x nanocomposite-based memristors. Memristive characteristics of the nanocomposite structures with different metal content are also comprehensively studied. Obtained results give every hope for bio-inspired operation of the future large memristor-based NS with reinforcement learning ability.