A nanofluid is a fluid containing suspended solid particles, with sizes of the order of nanometers. Normally the fluid has a low thermal conductivity compared to the suspended particles. Therefore introduction of these particles into the fluid increases the effective thermal conductivity of the system. It is of interest to predict the effective thermal conductivity of such a nanofluid under different conditions like varying particle volume fraction, varying particle size, changing fluid conductivity or changing fluid viscosity, especially since only limited experimental data are available. Also, some controversy exists about the role of Brownian motion in enhancing the nanofluid's thermal conductivity. We have developed a novel technique to compute the effective thermal conductivity of a nanofluid using Brownian dynamics simulation, which has the advantage of being computationally less expensive than molecular dynamics. We obtain the contribution of the nanoparticles towards the effective thermal conductivity using the equilibrium Green-Kubo method. Then we combine that with the thermal conductivity of the base fluid to obtain the effective thermal conductivity of the nanofluid, and thus are able to show that the Brownian motion contributes greatly to the thermal conductivity.