Recently, modelling and simulation have been used and applied to understand biological systems better. Therefore, the development of precise computational models of a biological system is essential. This model is a mathematical expression derived from a series of parameters of the system. The measurement of parameter values through experimentation is often expensive and time-consuming. However, if a simulation is used, the manipulation of computational parameters is easy, and thus the behaviour of a biological system model can be altered for a better understanding. The complexity and nonlinearity of a biological system make parameter estimation the most challenging task in modelling. Therefore, this paper proposes a hybrid of Particle Swarm Optimization (PSO) and Harmony Search (HS), also known as PSOHS, designated to determine the kinetic parameter values of essential amino acids, mainly aspartate metabolism, in Arabidopsis thaliana. Three performance measurements are used in this paper to evaluate the proposed PSOHS: the standard deviation, nonlinear least squared error, and computational time. The proposed algorithm outperformed the other two methods, namely Simulated Annealing and the downhill simplex method, and proved that PSOHS is a more suitable algorithm for estimating kinetic parameter values.