Methods that capture the features of single voxels of resting-state fMRI (RS-fMRI) could precisely localize the abnormal spontaneous activity and hence guide precise brain stimulation. As one of these metrics, the amplitude of low-frequency fluctuation (ALFF) has been used in numerous studies, however, it is frequency-dependent and the division of frequency bands is still controversial. Based on the well-accepted power law of time series, this study proposed an approach, namely, power spectrum slope (PSS), to characterize the RS-fMRI time series of single voxels. Two metrics, i.e., linear coefficient b and power-law slope b' were used and compared with ALFF. The reliability and validity of the PSS approach were evaluated on public RS-fMRI datasets (n = 145 in total) of eyes closed (EC) and eyes open (EO) conditions after image preprocessing, with 21 subjects scanned two times for test-retest reliability analyses. Specifically, we used the paired t-test between EC and EO conditions to assess the validity and intra-class correlation (ICC) to assess the reliability. The results included the following: (1) PSS detected similar spatial patterns of validity (i.e., EC-EO differences) and less test-retest reliability with those of ALFF; (2) PSS linear coefficient b showed better validity and reliability than power-law slope b'; (3) While the PPS showed less validity in most regions, PSS linear coefficient b showed exclusive EC-EO difference in the medial temporal lobe which did not show in ALFF. The power spectrum plot in the parahippocampus showed a "cross-over" of power magnitudes between EC and EO conditions in the higher frequency bands (>0.1 Hz). These results demonstrated that PSS (linear coefficient b) is complementary to ALFF for detecting the local spontaneous activity.