Proper contrast enhancement of colour images of retinal fundus is important to detect the eye diseases and its severity like in the case of diabetic retinopathy, as in a retinal fundus image contrast between different segments like retinal vessels, optic disk remains very low. In this paper, a novel parameterised variant of HE, called as Weighted and Entropy-Based Thresholded Histogram Equalisation (WEBTHE), has been proposed to enhance the retinal fundus images. WEBTHE is basically the combination of histogram modification-based HE variant and entropy-based thresholding method. Firefly Algorithm (FA) has been used to find the optimal values of the four parameters with diverse ranges corresponding to histogram modification of the proposed method by considering Peak Signal-to-Noise ratio (PSNR) as objective function. PSNR imparts full automation in computation to the method within reasonable time complexity. Experimental results show the superiority of the proposed method over other existing methods visually and mathematically. Copyright © 2018 Inderscience Enterprises Ltd.