A fitting procedure is proposed to establish two analytic approximate expressions for the complicated Rarker-Henderson (BH) diameter with Lennard-Joues potential in two temperature ranges. Considering that the differentiation is a process enlarging the errors and the integration decreasing the errors and that the derivative of BH diameter is important in the calculation of in ternal energy, we propose to tit the derivative directly, instead of usually fitting the original function and subsequently deriving its derivative. The simplicity and precision of two expressions developed are superior to the extensively deriving its derivative. The simplicity and precision of two expressions developed are superior to the extensively used expressions in literature. The one with following form only has an average fitting 0.0063% in the reduced temperature range (0.4≤Kt/S≤15), and can be extrapolated to a wider temperature range (0.4≤Kt/S≤50) with an average error 0.13%, which is d/ơ=1.1755+0.02878 In T -0.2072T1/4+0.00643T3/4.