Nuclear steam supply system (NSSS), which provides saturated or superheated steam to the secondary loop system for electricity or cogeneration, is central in a nuclear plant. The control of NSSS is important for the safe, stable and efficient plant operation. Nuclear superheated-steam supply system (Su-NSSS), which is equipped with an under moderated fission reactor and a once-through steam generator (OTSG) for producing superheated steam flow, is an important type of NSSS that widely applied in the nuclear plants based on the common large pressurized water reactors (PWR) and small modular reactors (SMRs) such as integral PWR (iPWR) and modular high temperature gas-cooled reactor (MHTGR). There is still very limited results for the control of Su-NSSS. Motivated by the gap between the importance and the lack of results in the field of Su-NSSS control, a model-free adaptive power-level control law is developed for Su-NSSSs with forced primary circulation in this paper. This new control law is free from physical and thermal-hydraulic parameters, is in the simple proportional-integral (PI) or proportional-differential (PD) form. To verify the feasibility of the newly-built Su-NSSS controller, it is applied to the NSSS control of a two modular high temperature gas-cooled nuclear plant with comparison to a specific MHTGR-based NSSS control law. Numerical simulation results show that this new control law can improve the transient performance of neutron flux and steam temperature in normal operation case, and can realize system resilience in some abnormal cases. (C) 2017 Elsevier Ltd. All rights reserved.