The on-axis two-frequency mutual coherence function (MCF) for beam waves propagating along a horizontal path in strong anisotropic atmospheric turbulence is theoretically formulated by making use of the extended Huygens-Fresnel principle. Based on this formulation, a new closed-form expression for the mean square temporal width of Gaussian-beam-wave pulses passing horizontally through strong anisotropic atmospheric turbulence is developed. With the help of this expression, the increments of mean square temporal pulse width due to strong anisotropic atmospheric turbulence under various conditions are further calculated. Results show that the increment of mean square temporal pulse width due to strong anisotropic atmospheric turbulence is basically proportional to the effective anisotropic factor in most situations of interest, with the possible exception of cases in which both the Fresnel ratio and spectral index become relatively small; increasing the effective anisotropic factor can reduce the number of the said exceptions; the turbulence-induced increment of mean square temporal pulse width enlarges as the spectral index increases with a fixed value of the nondimensional turbulence-strength parameter. It is also illustrated that a significant enlargement in the turbulence-induced increment of mean square temporal pulse width occurs by changing the Fresnel ratio from a large to a tiny value if both the effective anisotropic factor and spectral index are relatively small.