Based on the type expansion model, this paper integrates intellectual property rights protection(IPRP), the cutting-edge technology gap, and technological catch-up into a general equilibrium analysis framework to study the dynamic impact mechanism between IPRP and technological progress in latecomer countries. Research has shown that the technological catch-up effect generated by independent innovation and technological imitation will dynamically change with the cutting-edge technology gap, resulting in a “threshold effect” on the impact of intellectual property protection on technological catch-up related to the technological gap. The “threshold effect” provides a reasonable explanation for the paradox of IPRP promoting and inhibiting technological progress at the national level, as well as the temporal inconsistency of IPRP policies in developed countries across different historical periods. Moreover, the ability of a country to transform basic innovation and absorb national technology will significantly affect this threshold value. Numerical simulations show that a consistently low level of IPRP can lead technology latecomers into a “technology catch-up trap”. As the technological gap narrows, gradually tightening IPRP policies from loose to strict is the optimal dynamic technology catch-up strategy.This approach helps developing countries to break free from the “technology catch-up trap” and complete the process of technology catch-up. The conclusion regarding threshold effect was verified using cross-border panel data and a threshold model, and the empirical results were not affected by endogeneity issues and different measurement methods of core indicators. This study is helpful for China to formulate optimal dynamic IPRP policies according to the times and local conditions, promote independent innovation, and drive high-quality economic development.