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In this paper, we present a three-compartment of pharmacokinetics model with irreversible rate constants. The compartment consists of arterial blood, tissues and venous blood. Fick's principle and the law of mass action were used to develop the model based on the diffusion process. The model is modified into a fractional pharmacokinetics model with the sense of Caputo derivative. The existence and uniqueness of the model are investigated and the positivity of the model is established. The behaviour of the model is investigated by implementing numerical algorithms for the numerical solution of the system of fractional differential equations. MATLAB software is used to plot the graphs for illustrating the variation of drug concentration concerning time. Therefore, the numerical simulations of the model are presented for different values of α which verified the theoretical analysis. Besides, we also observed the pattern of the simulations at the three-compartment of the model by using different values of initial conditions.