Two-dimensional materials such as hexagonal boron nitride (h-BN), graphene, and transition metal dichalcogenides have drawn great attention in various fields of photonics and electronics. Among them, h-BN has recently emerged as a promising material platform to study integrated quantum photonics due to its ultrabright quantum light emission capabilities. However, the fundamental optical properties of h-BN have not yet been investigated in the visible and near-infrared (NIR) spectrum thoroughly. In this Letter, we report the refractive indices of h-BN thin films in the visible to NIR range. To the best of our knowledge, this is the first experimental observation of h-BN bi-refringence. Accurate parameters of refractive indices enable more precise design of h-BN-based photonic devices in the integrated photonics platforms.