Accurate modeling of thermospheric impact of high solar and geomagnetic activities is crucial for safeguarding our space-based infrastructure. However, current modeling capabilities are still unable to accurately predict thermospheric density, which is a key parameter for calculating satellite drags. In this paper, we performed global sensitivity analysis (GSA) for nitric oxide (NO)-related chemical reaction rates using the Global Ionosphere Thermosphere Model (GITM) during solar maximum and solar minimum conditions. We have performed GSA and uncertainty quantification (UQ) for the first time in GITM. GITM is a computationally expensive model; therefore, we employed a Gaussian process (GP)-based surrogate model to approximate the thermospheric states of GITM and inexpensively generate samples for Monte-Carlo-based Sobol analysis. We computed first-order (main effect) and total-order (total effect) Sobol’ sensitivity indices to quantify how the uncertainty associated with NO-related chemical reaction rate coefficients in GITM influences the variance of the NO density, NO cooling rate, temperature, and neutral density. Our study identified the most influential reaction rates the uncertainty of which contribute to the most uncertainty in estimating thermospheric states in GITM and provided important information for UQ within GITM to accurately estimate the thermospheric density. Our findings suggest that reducing the uncertainty in the reaction rates, particularly for RR43 ($NO + hv ightarrow N ({}^4 S) + O$), RR44 ($N({}^4 S) + O_2 ightarrow NO + O$), and RR5 ($N_2^+ + O ightarrow NO^+ ({}^2 D) + N ({}^2 D)$), should be prioritized to fix GITM’s response to variations in F10.7 solar flux.