Directed polymers in random potentials on higher dimensions at zero temperature are studied. The standard deviation of the lowest energy of the polymer varies as for length t and follows at saturation, where L is the system size. We obtain and in d = 5 + 1 and and in d = 6 + 1. We measure the end to end distance of the polymer and determine the dynamic exponent z directly by using the relation . It is consistent with the values estimated from . They satisfy the scaling relation very well. Our numerical results support that the upper critical dimension of the Kardar–Parisi–Zhang equation should be higher than d = 6 + 1. We also monitor the skewness and kurtosis of the energy distribution and find that they are in good agreement with the results for the discrete restricted solid-on-solid model. It seems that the normalized energy distribution is universal even in higher dimensions.