With a simple power-law approximation of high-redshift ($\gtrsim3.5$) star formation history, i.e., $\dot{\rho}_*(z)∝ [(1+z)/4.5]^{-α}$, we investigate the reionization of intergalactic medium (IGM) and the consequent Thomson scattering optical depth for cosmic microwave background (CMB) photons. A constraint on the evolution index $α$ is derived from the CMB optical depth measured by the {\it Wilkinson Microwave Anisotropy Probe} (WMAP) experiment, which reads $α≈2.18\lg{\mathscr{N}_{γ}}-3.89$, where the free parameter $𝒩_γ$ is the number of the escaped ionizing ultraviolet photons per baryon. Moreover, the redshift for full reionization, $z_f$, can also be expressed as a function of $α$ as well as $𝒩_{γ}$. By further taking into account the implication of the Gunn-Peterson trough observations to quasars for the full reionization redshift, i.e., $6\lesssim z_f \lesssim7$, we obtain $0.3\lesssimα\lesssim1.3$ and $80\lesssim𝒩_{γ}\lesssim230$. For a typical number of $∼4000$ of ionizing photons released per baryon of normal stars, the fraction of these photons escaping from the stars, $f_{\rm esc}$, can be constrained to within the range of $(2.0-5.8)%$. ; Comment: 10 pages, 4 figures, accepted for publication in JCAP