  Gaussian quasi-likelihood estimation of the parameter $\theta$ in the
square-root diffusion process is studied under high frequency sampling.
Different from the previous study of Overbeck and Ryd\'{e}n(1998) under
low-frequency sampling, high-frequency of data provides very simple form of the
asymptotic covariance matrix. Through easy-to-compute preliminary contrast
functions, a practical two-stage manner without numerical optimization is
formulated in order to conduct not only an asymptotically efficient estimation
of the drift parameters, but also high-precision estimator of the diffusion
parameter. Simulation experiments are given to illustrate the results.
