This work presents a modified version of the variable step size (VSS) least mean square (LMS) algorithm originally proposed by Kwong and Johnston [IEEE Trans. Signal Process. 40(7) (July 1992) 1633-1642]. The performance of the new algorithm, called noise resilient variable step size (NRVSS), is less sensitive than VSS to the power of the measurement noise. Its implementation requires only a very small increase in the computational complexity. Analytical models are derived for both NRVSS and VSS algorithms for Gaussian signals and small step-size fluctuations. Simulation results show that the NRVSS algorithm has approximately the same transient behavior as VSS but leads to lower steady-state excess mean-square errors as the signal-to-noise ratio (SNR) decreases. The NRVSS algorithm is specially indicated for adaptive interference reduction in biomedical applications.