The nozzle structural constraints of solid rocket motors significantly affect the response process of propellants under cook-off stimuli. To study the influence of nozzle throat diameter on the cook-off response of GAP-based solid propellants， a thermal load loading and control system for nozzle structural test pieces was designed and constructed. Using high-speed laser schlieren imaging technology， the entire cook-off response process of GAP-based propellants under the constraints of motor nozzle structures was observed. Additionally， the temperature of test pieces and the shock wave overpressure generated upon the ignition response were measured. The results indicate that the cook-off response of GAP-based solid propellant specimens with nozzle constraints can be divided into the following stages： softening and expansion of the propellant before ignition， and flame acceleration， deflagration-to-detonation transition （DDT）， casing failure， and deflagration process after ignition. The post-ignition response lasts only 0.5-2 milliseconds. From the pressure curve， it is evident that during the flame acceleration phase， the pressure grows slowly. When the nozzle throat diameter is relatively small， flow choking is more likely to occur. Once choking occurs， pressure and burning rate rapidly increase and reinforce each other， ultimately leading to deflagration-to-detonation transition. In contrast， for test pieces with large nozzle throat diameters， the rapid pressure rise cannot occur or be sustained， reducing the likelihood of deflagration-to-detonation transition and maintaining the structural integrity of test pieces.