An artificial neural network based on resistive switching memristors is implemented and simulated in LTspice. The influence of memristor variability and the reduction of the continuous range of synaptic weights into a discrete set of conductance levels is analyzed. To do so, a behavioral model is proposed for multilevel resistive switching memristors based on Al-doped HfO₂ dielectrics, and it is implemented in a spice based circuit simulator. The model provides an accurate description of the conductance in the different conductive states in addition to describe the device-to-device variability.