Abstract The fully memristive neural network consisting of the threshold switching (TS) material‐based electronic neurons and resistive switching (RS) one‐based synapses shows the potential for revolutionizing the energy and area efficiency in neuromorphic computing while being confronted with challenges such as reliability and process compatibility between memristive synaptic and neuronal devices. Here, a spiking convolutional neural network (SCNN) is constructed with the forming‐and‐annealing‐free V/VO x /HfWO x /Pt memristive devices. Specifically, both highly reliable RS (endurance >10 10 , on‐off ratio >10 3 ) and TS (endurance >10 12 ) are found in the same device by setting it at RRAM or selector mode with either the HfWO x or naturally oxidized VO x layers dominating the conductance tuning. Such reconfigurability enables the emulation of both synaptic and nonpolar neuronal behaviors within the same device. A V/VO x /HfWO x /Pt‐based hardware system is thus experimentally demonstrated at much simplified process complexity and higher reliability, in which typical neural dynamics including synaptic plasticity and nonpolar neuronal spiking response are imitated. At the network level, a fully memristive SCNN incorporating nonpolar neurons is proposed for the first time. The system level simulation shows competency in pattern recognition with a dramatically reduced hardware consumption, paving the way for implementing fully memristive intelligent systems.