Following the core conversion of Ghana’s miniature neutron source reactor (MNSR) from highly enriched uranium (HEU) to low-enriched uranium (LEU), there has been a change in the fuel composition, fuel, clad, and other reactor core parameters. Since the allowable core power in a nuclear reactor is limited by thermal considerations, this study presents transient analysis of the LEU core of Ghana Research Reactor−1 (GHARR-1). The transient study has been carried out using the Monte Carlo N-Particle code version 5 (MCNP5) and the Program for the Analysis of Reactor Transients (PARET)/Argonne National Laboratory (ANL) computational tools. The behavior of the reactor core at normal and accident conditions of large reactivity insertions was studied. Transient results obtained for accidental large reactivity insertions of 6.71 mk indicated that boiling might occur in the coolant because under such large reactivity insertions, the coolant temperature was close to the saturation temperature of the coolant. The results show that boiling will not occur in the core for other reactivity insertions of 1.94, 2.1, 2.99, 3.87, and 4.0 mk considering that the outlet coolant temperatures obtained are far below the saturation temperature of 100°C at a pressure of 1 atm. The clad and fuel meat temperatures obtained for all the reactivity insertions are far below the melting points of Zircaloy-4 clad material and UO2 fuel. The results of the power profiles obtained show that the reactor is inherently safe even under large reactivity insertion conditions. The results obtained were found to agree well with the available experimental results. Comparison of the results of the LEU core with the previous HEU core has shown that temperature rise in the LEU core is lower than that in the HEU core under reactor transient conditions.