Small modular reactors (SMRs) could be beneficial in providing electricity power safely and also be viable for applications such as seawater desalination and heat production. Due to its inherent safety features, the modular high temperature gas-cooled reactor (MHTGR) has been seen as one of the best candidates for building SMR-based nuclear power plants. Since the MHTGR dynamics display high nonlinearity and parameter uncertainty, it is necessary to develop a nonlinear adaptive power-level control law which is not only beneficial to the safe, stable, efficient and autonomous operation of the MHTGR, but also easy to implement practically. In this paper, based on the concept of shifted-ectropy and the physically-based control design approach, it is proved theoretically that the simple proportional-differential (PD) output-feedback power-level control can provide asymptotic closed-loop stability. Then, based on the strong approximation capability of the multi-layer perceptron (MLP) artificial neural network (ANN), a compensator is established to suppress the negative influence caused by system parameter uncertainty. It is also proved that the MLP-compensated PD power-level control law constituted by an experientially-tuned PD regulator and this MLP-based compensator can guarantee bounded closed-loop stability. Numerical simulation results not only verify the theoretical results, but also illustrate the high performance of this MLP-compensated PD power-level controller in suppressing the oscillation of process variables caused by system parameter uncertainty.