The propagation of General Model vortex Higher-order cosh-Gaussian beam (GMvHchGB) in a maritime atmospheric turbulence has been studied analytically by the extended Huygens-Fresnel principle. Based on the derived formulae, we performed numerical simulations to study the impact of maritime atmospheric turbulence on the properties of this beam under various beam parameter settings. GMvHchGB cannot keep its shape unchanged when it travels a long distance through this medium. The impact of the incident parameters as Gaussian waist, Cosh parameter, wavelength, hollowness and order of the beam are numerically analyzed.