Identifying heterogeneous treatment effects in observational studies is very difficult due to the fact that the outcome model or the treatment assignment model must be correctly specified. Taking advantages of semiparametric model, we use the single-index model to estimate heterogeneous treatment effects, which can allow the link function to be unbounded and have unbounded support. The link function is regarded as a point in an infinitely dimensional function space, and we can estimate the link function and the index parameter simultaneously. We establish the asymptotic properties of the proposed estimator. The finite-sample performance of the proposed estimator is evaluated through simulation studies. The proposed method is illustrated on real data from Pennsylvania in the USA to investigate the effect of maternal smoking during pregnancy on birth weight.