The baroreflex is one kind of homeostatic mechanisms to regulate acute blood pressure (BP) changes by controlling heartbeat interval (HBI). To quantify the effect of baroreflex, we suggested a new approach of analyzing Granger causality between systolic BP (SBP) and HBI. The index defined as baroreflex effectiveness (BRE) was generated by the hypothesis that more effectual baroreflex would be related to more effective Granger causal influence of SBP on HBI. Six obstructive sleep apnea (OSA) patients (apnea-hypopnea index, AHI ${geq}5$ events/hr) and six normal subjects participated in the study. Their SBP and HBI during nocturnal sleep were obtained from a non-invasive continuous BP measurement device. While the BRE ($mean{pm}SD$) of normal subjects was $47.0{pm}4.0%$, OSA patients exhibited the BRE of $34.0{pm}3.8%$. The impaired baroreflex function of OSA patients can be explained by the physiological mechanism associated with recurrent hypoxic episodes during sleep. Thus, the significantly lower BRE in OSA patients verified the availability of Granger causality analysis to evaluate baroreflex during sleep. Furthermore, the range of BRE obtained from normal subjects was not overlapped with that obtained from OSA patients. It suggests the potential of BRE as a new helpful tool for diagnosing OSA.