Space exploration is very important for the future of the earth and human beings as it may eliminate earth overpopulation and overcome diminishing of earth resources. One of the obstacles of the space exploration mission is the energy source for the spacecraft. One alternative is using a nuclear reactor as an energy source in spacecraft. A conceptual design of Indonesian Space Reactor (ISR) has been carried out to explore such a possibility. ISR is a liquid metal Na-78 K cooled space reactor with a fast neutron spectrum. It is designed to provide at least 500 kWth power for operating time more than 10 years at full power. The reactor uses 55% high-enriched uranium nitrate as fuel. The ISR hexagonal core is comprised of 61 fuel pins and is designed in the form of a hollow cylinder with an individual cooling channel in each fuel pin. The reactor is also equipped with spectral shift absorbers (SSA) made of Re and Mo-30Re alloy to control the reactivity. Neutronic calculations have been performed to obtain optimum design parameters without compromising safety requirements. These design parameters include variation in uranium enrichment, reactor dimension, reflector thickness and control drum (absorber) design and dimension. The accepted reactor design has an excess reactivity of 4023 ± 9 pcm and shutdown margin of 4852 ± 9 pcm and the reactor is estimated to have a lifetime of 28 years. The temperature and void reactivity coefficients are all negative, implying inherent safety. Several accident scenarios were also considered in this work, both during launch failure and normal operation. It is found that to keep the reactor subcritical for a submerged reactor following a launch failure, the reflector segment should be discarded. Meanwhile, some portions of fuel pins should be removed from the core during operational accidents.