In support of more efficient utilization of solar and nuclear energy in power generation, the present work proposes a conceptual design of a hybrid nuclear-solar power system (HNSPS) for on-demand power supply, based on a parallel thermal integration of small modular reactors with commercialized molten-salt concentrating solar power tower plants. A cost-effective thermal energy storage system is employed as a thermal coupling and a heat dispatcher to coordinate both nuclear heat and solar heat with power demands. The overall configuration and operation strategy of the hybrid system are elaborated. A numerical model of the hybrid system is developed based on the circulation of molten-salt. Using the model, a 7-day performance analysis of the hybrid system with different considerations are conducted. Effects of key design parameters on system performances are investigated by a parametric study. A customized evaluation parameter, named as "design score", is defined to assess the suitability of the designed configurations. The performance analysis shows that the integration of nuclear power with concentrating solar power allows the system to be less dependent on heat dispatch to achieve required power regulations, comparing to a standalone CSP plant with an equivalent power capacity. The parametric study indicates that a higher heat generation utilization of the hybrid system requires a larger TES and a smaller heliostats field, while a higher power supply efficiency of the hybrid system is accompanied with a larger TES, a larger heliostats field, and a higher nuclear power capacity proportion. The optimum design configuration of a 200 MWe HNSPS is estimated to have a nuclear power capacity proportion of 50%, a theoretical thermal energy storage duration of 14.8 h, and a heliostats field with a solar multiple of 1.27. This configuration can completely satisfy the power demand without any heat generation curtailment during the 7-day operation. The obtained results allow the HNSPS to be considered as a promising non-carbon-emitting power generation system for on-demand power supply.