A τ lepton can be produced in a charged current interaction by cosmic ray tau neutrino with material inside a mountain. If it escapes from the mountain, it will decay and initiate a shower in the air, which can be detected by an air shower fluorescence/Cherenkov light detector. Designed according to such a principle, the Cosmic Ray Tau Neutrino Telescope (CRTNT) experiment, located at the foothill of Mt. Balikun in Xinjiang, China, will search for very high-energy cosmic τ neutrinos from energetic astrophysical sources by detecting those showers. This paper describes a Monte Carlo simulation for a detection of τ events by the CRTNT experiment. Ultra-high-energy cosmic ray events are also simulated to estimate the potential contamination. With the CRTNT experiment composed of four detector stations, each covering 64 • × 14 • field of view, the expected event rates are 28.6, 21.9 and 4.7 per year assuming AGN neutrino flux according to Semikoz et. al. 2004, MPR AGN jet model and SDSS AGN core model, respectively. Null detection of such τ event by the CRTNT experiment in one year could set 90% C.L. upper limit at 19.9(eV · cm −2 · s −1 · sr −1 ) for E −2 neutrino spectrum.PACS numbers: 96.85. Ry, 96.40.Pq, 98.70.Sa, 95.55.Vj