In this article, we aim to prove strong and $\Delta$-convergence theorems of Noor iterative process for generalized Suzuki nonexpansive mappings (GSNM) on uniform convex hyperbolic spaces. Due to the richness of uniform convex hyperbolic spaces, the results of this paper can be used as an extension and generalization of many famous results in Banach spaces together with $CAT\left(0\right)$ spaces.