In this article, exponentiated U-quadratic distribution (EUq) is proposed by exponentiation procedure. The quantile function and r th moment of the new model are computed. Estimation of parameter by the alternative maximum likelihood and estimation based on percentiles are established and compare their performances through numerical simulations. The results show that both methods are suitable for the parameter estimation of EUq distribution. A real data set is used to compare the fit of the two proposed estimation method using Kolmogorov Smirnov test (KS).