In this thesis we have analyzed bulk thermodynamic properties of QCD at high temperature and small but non-vanishing baryon density on lattices. We have used the integration method to calculate the pressure at zero chemical potentials. The thermodynamic quantities are normalized such that they vanish at zero temperature. The zero temperature calculations are thus needed for both calibrating the lattices and the subtraction procedure for the normalizations. In this study, we have scanned a wide range of temperature and constructed a line of constant physics, on which the strange pseudo-scalar meson mass and kaon mass are kept at their physical values and the light pseudo-scalar meson mass is about 220 MeV. Our calculations are mostly carried out on lattices with cut-offs a = 1/4T and 1/6T, where T is the system temperature. All thermodynamic quantities, such as pressure, energy density as well as energy-momentum trace anomaly, show small cut-off effects. We have also calculated the trace anomaly at high temperatures on N = 8 lattices to check that the lattice cut-off effects are under control. In order to study the QCD thermodynamics at small chemical potentials, we have used the Taylor expansion method. The pressure is expanded in terms of quark chemical potentials and the expansion coefficients at zero chemical potentials are calculated up to the fourth order on both N = 4 and 6 lattices. Using these coefficients thermodynamic quantities, e.g. pressure and number densities, have been constructed and shown.