This paper proposes the design of an adaptive filter in stochastic circuits. The proposed circuit requires lower area and power than a conventional stochastic implementation. In the proposed design, the stochastic multiplier is implemented by an XNOR gate, as in a conventional scheme. However, the stochastic adder based on a multiplexer is not a very efficient implementation due to the three required stochastic number generators (SNGs) and the iterative operation required in the adaptive filter. Thus, a novel stochastic adder using a counter and a post processing unit is proposed. This adder avoids the use of SNGs, therefore it incurs a smaller area and power, while operating faster than the conventional (multiplexer-based) stochastic adder. In terms of accuracy and hardware efficiency, simulation results show that the adaptive filter using the proposed stochastic design outperforms the conventional stochastic implementation using linear feedback shift register (LFSR) based SNGs. Specifically, the proposed design consumes 35.81% less dynamic power and 21.34% less area than an LFSR-based implementation at a slightly higher accuracy.@en