Magnetic-field-induced Josephson-junction (JJ) behavior in a highly transparent weak link was observed at the 5\ifmmode^\circ\else\textdegree\fi{} tilt low angle grain boundary (LAGB) in a $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ film. The magnetic field dependence of current density-voltage curves showed that Abrikosov Josephson (AJ) vortices exist in the LAGB. Both JJ and flux-flow (FF) behaviors were observed in a single LAGB depending on the temperature and magnetic field. The crossover from FF to JJ arose from the spread of the phase variation along the junction when the AJ vortex cores overlapped at ${B}^{*}={\ensuremath{\phi}}_{0}∕{(4.4l)}^{2}$, where $l$ is the characteristic length of AJ vortex.