The 3-D multi-fluid BATS-R-US MHD code (MF-MHD) is coupled with the 3-D Mars Thermospheric General Circulation Model (MTGCM). The ion escape rate from the Martian upper atmosphere is investigated by using a one-way coupling approach, i.e., the MF-MHD model incorporates the effects of 3-D neutral atmosphere profiles from the MTGCM model. The calculations are carried out for two cases with different solar cycle conditions. The calculated total ion escape flux (the sum of three major ionospheric species, $O^+$, $O_2^+$ and $CO_2^+$) for solar cycle maximum conditions ($6.6 \times 10^{24}$ $s^{-1}$) is about 2.6 times larger than that of solar cycle minimum conditions ($2.5 \times 10^{24}$ $s^{-1}$). Our simulation results show good agreement with recent observations of $2 ∼ 3 \times 10^{24}$ $s^{-1}$ ($O^+$, $O_2^+$ and $CO_2^+$) measured near solar cycle minimum conditions by Mars Express (MEX). An extremely high solar wind condition is also simulated which may mimic the condition of CMEs or CIRs passing Mars. Simulation results show that it can lead to a significant value of the escape flux as large as $4.3 \times 10^{25}$ $s^{-1}$.