With reference to the experimental observations by Yanagida and his co-workers concerning actomyosin interaction during muscle contraction processes, we propose a phenomenological model for the sliding of the myosin head on the actin filament, in which the myosin head is viewed as an active Brownian particle in a periodic, elastic-type potential subject to tilting. The sample paths thus obtained are qualitatively alike to those experimentally recorded. Furthermore, our model is proved to be susceptible of a consistent parameters regulation yielding step frequencies, mean step dwell time and dwell time distribution in excellent agreement with the experimental evidence.