This paper examines the construction of a parameter-dependent voltage prediction model for a primary Zinc-air cell prototype, focusing on its response time when subjected to multiple step-wise discharge current levels. Laboratory tests have revealed that the dynamic response’s time constant varies with discharge current, a phenomenon not adequately addressed in previous analyses. The current research aims to contribute to the existing knowledge by employing a piecewise current profile during a single cell discharge and conducting an identification-type analysis of the relationships between the system’s time constants and other state and input variables. The findings presented in this paper hold significant potential for integration into Battery Management Systems and, in the long term, for addressing the inverse problem of State-of-Charge estimation.