Heat pipe cooled reactors (HPR) utilize heat pipes to export the fission heat. Compared to conventional reactors, HPR eliminates the coolant loop. Therefore, HPR has compact structure, simple power system and higher inherent safety, which is an ideal choice to meet the power requirements of decentralized markets. To reduce the reactivity control mechanism, this paper presents a conceptual design of the low excess reactivity heat pipe reactor (LRHPR). The breeding capability of core can be improved by reducing the pitch-to-diameter ratio of fuel element during operation because the absorbing neutrons of coolant are reduced and the more 238U in the core is bred into the fissile 239Pu in the depletion process. The neutronics calculations of core are performed with the Monte Carlo codes OpenMC. Results show that the 45 MWth LRHPR with the pitch-to-diameter ratio of 1.1442 can continuously operate for about 15 years. The corresponding keff is first increased and then decreased during operation because the bred 239Pu in the core provides a higher positive reactivity during the early operation and the core has a lower inventory of excess nuclear fuel during the next operation. The corresponding maximum swing range of excess reactivity of core is less than 0.2% during the whole operation. The total temperature reactivity coefficients of core are also negative, indicating that the core has inherent safety feature. Therefore, few reactivity control in the core is required during operation. Besides, a center control rods device is designed based on the reactor core. When the control rods device is entirely inserted into core, the keff of core is less than 0.98, indicating that the reactor core has sufficient margin to ensure shutdown in case of an accident.