The Bayesian Confidence Propagation Neural Network (BCPNN) has been implemented in a way that allows mapping to neural and synaptic processes in the human cortexandhas been used extensively in detailed spiking models of cortical associative memory function and recently also for machine learning applications. In conventional digital implementations of BCPNN, the von Neumann bottleneck is a major challenge with synaptic storage and access to it as the dominant cost. The memristor is a non-volatile device ideal for artificial synapses that fuses computation and storage and thus fundamentally overcomes the von Neumann bottleneck. While the implementation of other neural networks like Spiking Neural Network (SNN) and even Convolutional Neural Network (CNN) on memristor has been studied, the implementation of BCPNN has not. In this paper, the BCPNN learning rule is mapped to a memristor model and implemented with a memristor-based architecture. The implementation of the BCPNN learning rule is a mixed-signal design with the main computation and storage happening in the analog domain. In particular, the nonlinear dopant drift phenomenon of the memristor is exploited to simulate the exponential decay of the synaptic state variables in the BCPNN learning rule. The consistency between the memristor-based solution and the BCPNN learning rule is simulated and verified in Matlab, with a correlation coefficient as high as 0.99. The analog circuit is designed and implemented in the SPICE simulation environment, demonstrating a good emulation effect for the BCPNN learning rule with a correlation coefficient as high as 0.98. This work focuses on demonstrating the feasibility of mapping the BCPNN learning rule to in-circuit computation in memristor. The feasibility of the memristor-based implementation is evaluated and validated in the paper, to pave the way for a more efficient BCPNN implementation, toward a real-time brain emulation engine.