  The nano-bridge junction (NBJ) is a type of Josephson junction that is
advantageous for the miniaturization of superconducting circuits. However, the
current-phase relation (CPR) of the NBJ usually deviates from a sinusoidal
function which has been explained by a simplified model with correlation only
to its effective length. Here, we investigated both measured and calculated
CPRs of niobium NBJs of a cuboidal shape with a three-dimensional bank
structure. From a sine-wave to a saw-tooth-like form, we showed that deviated
CPRs of NBJs can be described quantitatively by its skewness {\Delta}{\theta}.
Furthermore, the measured dependency of {\Delta}{\theta} on the critical
current {I_0} from 108 NBJs turned out to be consistent with the calculated
ones derived from the change in geometric dimensions. It suggested that the
CPRs of NBJs can be tuned by their geometric dimensions. In addition, the
calculated scaling behavior of {\Delta}{\theta} versus {I_0} in
three-dimensional space was provided for the future design of superconducting
circuits of a high integration level by using niobium NBJs.
