The effect of wick structure on the performance of capillary-driven heat pipes is analyzed numerically. Three types of wick structure are investigated: copper screen, sintered steel, and sintered copper. Using lattice Boltzmann method, the entire heat pipe is modeled including heat transfer through the wall and heat and mass transfer in the liquid-wick and vapor regions. Comparison between the present model and analytical results available in the literature shows excellent agreement. The liquid velocity profiles and temperature distribution in the wall are also presented for different working fluids and discussed. Comparison is made between performance of heat pipes with different wick structures and working fluids. Results indicate better performance, with a factor up to 1.7, of heat pipes using water as working fluid with sintered copper structure than with other wick structures. In addition, it is found that the larger the liquid's radial velocity, the less the thermal resistance at given heat input power. Both a simple equivalent resistance circuit and numerical data suggest strongly that the most impactive fluid properties on the heat pipe performance seem to be the latent heat of vaporization, the molecular mass, the change rate of the saturation pressure with respect to temperature, and the conductivity of its liquid phase.