This paper considers the asymptotic solutions of a class of singularly perturbed equations for larger parameter with turning point of $n$-th order. Firstly, the outer solution when $n$ is odd or even, respectively, is obtained by using the Liouville-Green transformation. Then, the interior layer solution near the $x=0$ when $n$ is odd or even is constructed by introducing the stretching transformation and using the Bessel function. Finally, the arbitrary constants for the outer solution and interior layer solution are determined by using the matching principle. Thus, we obtain the uniformly valid asymptotic expression of the equation.