Causal-effect discovery plays an essential role in many disciplines of science and real-world applications. In this paper, we introduce a new causal discovery method to solve the classic problem of inferring the causal direction under a bivariate setting. In particular, our proposed method first leverages a flow model to estimate the joint probability density of the variables. Then we formulate a novel evaluation metric to infer the scores for each potential causal direction based on the variance of the conditional density estimation. By leveraging the flow-based conditional density estimation metric, our causal discovery approach alleviates the restrictive assumptions made by the conventional methods, such as assuming the linearity relationship between the two variables. Therefore, it could potentially be able to better capture the complex causal relationship among data in various problem domains that comes in arbitrary forms. We conduct extensive evaluations to compare our method with decent causal discovery approaches. Empirical results show that our method could promisingly outperform the baseline methods with noticeable margins on both synthetic and real-world datasets.