According to the generalized Huygens-Fresnel diffraction integral, the dynamic evolution of a noncanonical optical vortex with phase topological charge (topological charge) of m=+1 and +2 in the background of a Gaussian beam passing through a tilted lens is studied. It is found that after passing through the tilted lens,the noncanonical strength and topological charge of the noncanonical optical vortex with topological charge of m=+1 remain unchanged, while the noncanonical optical vortex with topological charge of m=+2 will split into two noncanonical optical vortices with the same noncanonical strength (the noncanonical strength is equal to the noncanonical strength of the noncanonical optical vortex with topological charge of +2 at the initial plane) and the same topological charge of m=+1 due to the influence of noncanonical strength. The position of the noncanonical optical vortex after passing through the tilted lens depends on the relative propagation distance, off-axis parameter, noncanonical parameters, tilt coefficients, waist width, and the sum of the topological charge remains unchanged during the propagation.