Functional MRI studies have started the hemodynamic responses of the placenta and fetal brain using maternal hyperoxia. While most studies have focused on analyzing the changes in magnitude of fMRI signals, few studies have analyzed the latency and duration of responses to hyperoxia. This paper proposes a linear convolution model of fetal circulation where a chain of responses to maternal hyperoxia are produced in the placenta and fetal brain. Specifically, an impulse response to hyperoxia was modeled as the hemodynamic response function (HRF) which consists of multiple gamma functions. Both time-to-peak and full width at half maximum of HRF were estimated using simulated annealing (SA). A Monte Carlo simulation was carried out to evaluate the performance of the SA-based method for estimating both parameters. Finally, we provided an example of estimating HRFs from fMRI time series of the placenta and fetal brain acquired during maternal hyperoxia in vivo.