By using molecular dynamics (MD) simulation method, we studied temperature dependence and nanoparticle-size dependence of thermal conductivity of diamond nanoparticles. In order to get more reliable results, equilibrium molecular dynamics (EMD) method was applied. We set a relatively long integral time in the calculation of heat current autocorrelation function (HCACF), and got convergent results. Our results indicate that due to size effect, thermal conductivity of diamond nanoparticles is smaller than the one of bulk diamond. As temperature varies, thermal conductivity shows a peak value at 61.6K, which behaves a little different from bulk diamond. As particle size increases, thermal conductivity increases; from the tendency of our plot, we predict that thermal conductivity of diamond nanoparticles will converge at the value of bulk diamond with a proper size. More work will be done on this prediction in our future researches.