Cannabidiol (CBD) appears to possess some neuroprotective properties, but experimental data are still inconsistent. Therefore, this in vitro study aimed to compare the effects of CBD in a wide range of concentrations on oxidative stress and excitotoxic-related cell damage. Results showed that low concentrations of CBD ameliorated the H2O2-evoked cell damage of primary cortical neuronal cell culture. However, higher concentrations of CBD alone (5–25 μM) decreased the viability of cortical neurons in a concentration-dependent manner and aggravated the toxic effects of hydrogen peroxide (H2O2). Neuroprotection mediated by CBD in primary neurons against H2O2 was not associated with a direct influence on ROS production nor inhibition of caspase-3, but we found protective effects of CBD at the level of mitochondrial membrane potential and DNA fragmentation. However, CBD had no protective effect on the glutamate-induced cell damage of cortical neurons, and in higher concentrations, it enhanced the toxic effects of this cell-damaging factor. Likewise, CBD, depending on its concentration, at least did not affect or even enhance cortical cellular damage exposed to oxygen–glucose deprivation (OGD). Finally, we showed that CBD in submicromolar or low micromolar concentrations significantly protected human neuronal-like SH-SY5Y cells against H2O2- and 6-hydroxydopamine (6-OHDA)-induced cell damage. Our data indicate that CBD has a dual effect on oxidative stress-induced neuronal death-in low concentrations, it is neuroprotective, but in higher ones, it may display neurotoxic activity. On the other hand, in excitotoxic-related models, CBD was ineffective or enhanced cell damage. Our data support the notion that the neuroprotective effects of CBD strongly depend on its concentration and experimental model of neuronal death.