This work aims at examining the influence of lorazepam, an anxiolytic drug with sedative effects, on brain activity and specifically on EEG Fractal Dimension (FD). The main objective is to clarify the reasons for FD increase after drug intake and to establish a relationship between FD and EEG energy bands. 14 healthy subjects that received either 2.5mg of lorazepam (verum case) or placebo (placebo case) participated in the experiment. 20 EEG channels have been used. One-way ANOVA test revealed that lorazepam increases significantly both FD (p = 0) and beta energy band (p = 1.18E-013 for beta1 band and p = 2.29E-011 for beta2 band) and decreases alpha energy band (p = 0.05 for alpha1 and p = 0.0036 for alpha2), whereas there was not any significant difference on placebo subjects before and after drug intake. Moreover, correlation results indicate that there is a strong correlation between FD and beta energy band (mean correlation coefficient = 0.4120 for beta1 and 0.5358 for beta2) and a negative correlation between FD and alpha1 energy band (mean correlation coefficient -0.4930). Additionally, the mean correlation coefficient between FD and a combination of the different energy bands (beta1+beta2-alpha1) is 0.6185 and reaches value 0.684 for channels F7, T6, P4. These results indicate that there is a relationship between EEG energy bands and FD and provide a link between the classic spectral analysis and the complexity analysis.