Summary: Given harmonic mappings \(f(z)=h(z)+\overline{g(z)}\) on the unit disk \(D=\{z|\, |z|<1\}\), where \(h(z)\) and \(g(z)\) are analytic functions on the unit disk \(D\), with \(f(0)=0, \ \lambda_f(0)=1\) and \(\Lambda_f\leqslant\Lambda\), by introducing one complex parameter \(\lambda\), we consider the properties of the harmonic mappings \(F_\lambda (z)=h(z)+\lambda \overline{g(z)}\) and analytic functions \(G_\lambda(z)=h(z)+\lambda g(z)\) with \(|\lambda|=1\) and obtain the sharp estimate on univalent radius for \(F_\lambda (z)\) and \(G_\lambda(z)\). As an application, we also obtain a better estimate on Bloch constant for some \(K\)-quasiregular harmonic mappings on the unit disk \(D\).