Based on the one-dimensional periodic and Fibonacci-like waveguide arrays, we experimentally investigate localized quantum walks (QWs), both in the linear and nonlinear regimes. Unlike the ballistic transport behavior in conventional random QWs, localization of QWs is obtained in the Fibonacci-like waveguide arrays both theoretically and experimentally. Moreover, we verify the enhancement of the localization through nonlinearity-induced effect. Our work provides a valid way to study localization enhancement in QWs, which might broaden the understanding of nonlinearity-induced behaviors in quasi-periodic systems.