By using the Wigner distribution function and the generalized Huygens-Fresnel principle, an analytical formula, which is independent on specific spatial power spectrum of the refractive index fluctuations of atmosphere, for beam width of partially coherent beams propagating through atmospheric turbulence along a slant path is derived. Then, taking the partially coherent flat-topped (PCFT) beams as a typical example, the analytical formula for beam width spreading of PCFT beams propagating through atmospheric turbulence along a slant path is given. Consequently, numerical calculations and analysis are carried out by considering the vertical distribution models of atmospheric structure constant of refractive index in Hefei, and the results for a slant path are compared with those for a horizontal path. Research results demonstrate that the beam width is not only related to the beam order, the degree of spatial coherence, the waist radius, the intensity of turbulence and the propagation distance but also closely to the zenith angle. With the higher beam order, the worse spatial coherence of the beam and the smaller zenith angle, the spreading of beam width is less affected by the turbulence. When the zenith angle is less than 60°, the influence of the atmospheric turbulence to the beam width along the slant path is much smaller than that along the horizontal path.