<p>The authors provide a method for determining liouvillian solutions of a class of first-order algebraic ordinary differential equations (AODEs). In more details, if a first-order AODE is of genus zero, the authors prove that its liouvillian solutions can be found via a class of quasi linear first-order ordinary differential equations by means of associated field of algebraic functions and rational parametrizations. In addition, the authors propose an algorithm to determine the reduced form of a certain first-order AODE by means of power transformations. This induces a novel approach for finding liouvillian solutions of first-order AODEs of positive genera whose reduced form are of genus zero. Some examples are given to illustrate the method in the affirmative cases.</p>