This paper addresses the staffing problem of a multi-skill call center with prioritized and patient customers based on a queuing model for minimizing staffing costs subject to service level requirements and determining the optimal number of agents. The model includes three types of calls and four groups of agents with different skills. Initially, a method for describing the state space is presented, followed by obtaining state-transition rates of the study model from 𝑀𝑀/𝑀𝑀/𝑐𝑐 and 𝑀𝑀/𝑀𝑀/𝑐𝑐/𝑐𝑐 queuing systems. Equations for steady-state probabilities and service level computation are derived. A staffing calculation model for optimal agent numbers in each group is then formulated. An algorithm is proposed to find solutions, and its process is outlined. Finally, a numerical example is provided to analyze the system's sensitivity to several factors.