The Fermi arcs of topological surface states in the three-dimensional multi-Weyl semimetals on surfaces by a continuum model are investigated systematically. We calculated analytically the energy spectra and wave function for bulk quadratic-and cubic-Weyl semimetal with a single Weyl point. The Fermi arcs of topological surface states in Weyl semimetals with single-and double-pair Weyl points is investigated systematically. The evolution of the Fermi arcs of surface states variating with the boundary parameter are investigated and the topological Lifshitz phase transition of the Fermi arc connection is clearly demonstrated. Besides, the boundary condition for the double parallel flat boundary of Weyl semimetal is deduced with a Lagrangian formalism.