Emerging ferroelectric tunnel memristors show large OFF/ON resistance ratio (>100) and high operation speed (~10ns), promising to be widely applied in the future synapse-like systems. In this paper we propose a neuromorphic network with ferroelectric tunnel memristor. This network is arranged with classical crossbar topology, in which each crosspoint forms a synapse consisting of a MOS transistor and a memristor. Based on this architecture, we design a spike-timing dependent plasticity (STDP) scheme and a parallel supervised learning circuit. Using a compact model of ferroelectric tunnel memristor and CMOS 40nm design kit, we perform transient simulation to validate the functionality of the proposed STDP and learning circuit. Simulation results show the potential of our neuromorphic network in low power (~100nA or ~1μA) and high speed (μs or ~100ns) computing system.