In the present paper, the influences of cutting parameters on surface roughness in wire electric-discharge machining of (WEDM) process of particle-reinforced aluminium AA6061 alloy composite are investigated. The composites are produced using 15% wt. B$_{4}$C fraction using powder metallurgy. Experimental trials are performed based on Taguchi L18 ($2^{1} \times 3^{2}$) with a mixed orthogonal array, and the WEDM cutting parameters are optimized for the best surface quality. The investigation results are evaluated by response surface plots and main effect graphs. The machined surface of the metal matrix composite is investigated using scanning electron microscopy (SEM) micrographs. The effect of WEDM machining variables are determined using analysis of variance (ANOVA). The analysis result shows that the most significant cutting parameter is peak current for surface roughness. The SEM and optical micrographs indicate that the reinforced B$_{4}$C particles are homogeneously distributed in the matrix structure. Mathematical models are also generated using regression analysis for the surface roughness. Confirmation tests are carried out to determine the prediction performance of the mathematical models, and the surface roughness is predicted with an acceptable mean squared error.