Donald and Hsu (2014) studied estimation and inference of the counterfactual distribution and quantile functions in the binary treatment model. We extend their work to the continuous treatment model. Specifically, we propose a weighted regression estimator for the counterfactual distribution but we estimate the weighting function from a covariate-balancing equation by maximizing a globally concave criterion function. We estimate the quantile function by inverting the estimated counterfactual distribution. To test the distributional effect, we consider the (uniform) confidence band, the sup and L2 distance and particularly the Mann-Whitney test. We also consider the stochastic dominance test for the distributional effect and the L2 test for the constant quantile. A simulation study reveals that our tests have a good finite sample performance, and an application shows they have some practical value.