Abstract: A new class of alpha skew power normal distribution is proposed, such that alpha skew normal distribution and power normal distribution are special cases. Its moment, skewness, kurtosis, Fisher information matrix, maximum likelihood estimator and the generation algorithm of random number are given. Extensive simulation experiments show that the maximum likelihood estimator of parameters has good asymptotic statistical properties, the distribution fitting results of a group of real data sets show that alpha skew power normal distribution has better fitting effect than normal distribution, skew normal distribution, power normal distribution and alpha skew normal distribution.