The dependence of the mean kinetic energy of laser-accelerated relativistic electrons (REs) on the laser intensity, so-called ponderomotive scaling, explains well the experimental results to date; however, this scaling is no longer applicable to multi-picosecond (multi-ps) laser experiments. Here, the production of REs was experimentally investigated via multi-ps relativistic laser–plasma-interaction (LPI). The lower slope temperature shows little dependence on the pulse duration and is close to the ponderomotive scaling value, while the higher slope temperature appears to be affected by the pulse duration. The higher slope temperature is far beyond the ponderomotive scaling value, which indicates super-ponderomotive REs (SP-REs). Simulation and experimental evidence are provided to indicate that the SP-REs are produced by LPI in an under-critical plasma, where a large quasi-static electromagnetic field grows rapidly after a threshold timing during multi-ps LPI.