An analytical potential for cylindrical pores has been derived by introducing a variational method into the integration for the calculation of the interaction energy between the wall molecules and a test molecule, all of which are represented by Lennard-Jones potential. The model proposed gives good fit to the results from the cylindrical surface model and the pseudoatom model. To test the potential proposed rigorously, we have carried out grand canonical ensemble Monte Carlo(GCMC) simulation of nitrogen in the MCM-41 pore at 77 K, and compared the simulated adsorption isotherm with the experimental data reported in the literature. The simulated isotherm from our model is in almost qualitative agreement with experiment. Consequently, the model proposed provides an explicit and accurate description of cylindrical pores represented by the Lennard-Jones potential. Moreover, the model can be easily applied to a variety of cylindrical pores, ranging from cylindrical surface to finite thickness walls, in both theoretical studies and computer simulations.