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This paper presents a refined version of the M/G/~ busy-server process described in IEEE J. Select. Areas Commun., 16(5) (1998) 733-748 for VBR video modelling, with emphasis on a refined fitting approach of marginal distribution. First we suggest using normal mixture distribution instead of Gamma-Pareto distribution to model the marginal distribution for greater flexibility and accuracy. Second, we retune the parameter value of the Poisson input process to ensure smooth distribution transformation. Experimental results indicate that our model gives closer estimate to the empirical cell loss behaviour than the original model. Also, its performance is more consistent than other uni-distribution models like Gamma and lognormal, when fitting a wide variety of video sequences.