Adaptive filters are employed in many signal pro- cessing and communications systems. Commonly, the design and analysis of adaptive algorithms, such as the least mean-squares (LMS) algorithm, is based on the assumptions that the signals are wide-sense stationary (WSS). However, in many cases, including, for example, interference-limited wireless communications and power line communications, the considered signals are jointly cyclostationary. In this paper we propose a new LMS-type algorithm for adaptive filtering of jointly cyclostationary signals using the time-averaged mean-squared error objective. When the considered signals are jointly WSS, the proposed algorithm specializes to the standard LMS algorithm. We characterize the performance of the algorithm without assuming specific distributions on the considered signals, and derive conditions for convergence. We then evaluate the performance of the proposed algorithm, called time-averaged LMS, in a simulation study of practical channel estimation scenarios. The results show a very good agreement between the theoretical and empirical performance measures.