Optics lattice clock is a hot topic in the researches of frequency standard and metrology. Neutral mercury atom is one of the most promising candidates for optical lattice clock. Due to its large atomic number, mercury atom is insensitive to black body radiation, which is the severe limitation for developing the optical lattice clocks. To realize the optical lattice clock of neutral mercury atoms, the first step is to implement laser-cooling and trapping of neutral mercury atoms. The cooling transition of mercury atom is 1S0-3P1 transition. The wavelength is 253.7 nm, the line width is 1.27 MHz, and the saturation intensity is 10.2 mW/cm2. Quantum projection noise (QPN) is an important parameter that affects optical lattice clock. Increasing the loading rate of magneto-optical trap (MOT) can help lower the QPN, thereby improving the performance of optical lattice clock. In this work, we calculate the scattering force of deep UV cooling laser, which is exerted on mercury atom in our single chamber MOT, and numerically simulate the one-dimensional motion of the atom in the MOT. It gives us the capture velocity under optimized parameters of the MOT. Then we calculate the loading rate of three-dimensional MOT by a high efficient random sampling method. According to the rate equation of MOT, the loading rate is proportional to the atom number of the steady state, which is the accessible parameter in the experiment. An experimental setup of MOT is established with a high vacuum system and a frequency quadrupled semiconductor laser system. The fluorescence imaging on an EMCCD gives the atom number in the MOT. We also calibrate the vapor density of background mercury gas in the vacuum, and measure the atom number in a steady MOT. We numerically simulate and experimentally study the influences on the atom number on the parameters of MOT, such as laser intensity, laser detuning and magnetic field gradient. The calculated results are in consistent with the experimental results. We also find the optimized parameters to maximize the loading rate. The numerical simulation also gives some results beyond current experimental condition, especially for laser intensity. From the simulations we obtain the optimized MOT parameter and relation for laser cooling of neutral mercury atom. Especially, current deep UV cooling laser with 20 mW of power does not have enough power to enhance the loading rate. These results are rather valuable for designing the next generation of optical lattice clocks for neutral mercury atoms.