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Fluid substitution is a crucial tool in geophysical exploration, which is widely used in reservoir characterization, time-lapse seismic monitoring, rock physics analysis, etc. For weakly transversely isotropic media with a vertical symmetry axis (VTI), we simplified the stiffness constant C3333 for the vertical P-wave velocity, based on the Brown-Korrigna anisotropic fluid substitution equations. The proposed approximate anisotropic fluid substitution equation can be estimated using the Brown-Korringa isotropic fluid substitution equation, with a correction that includes a first-order Thomsen anisotropic δ term. In the special case that the mean compressibility equals the grain compressibility, the approximate formulas can be further simplified into expressions derived by Mavko and Bandyopadhyay, based on Gassmann’s anisotropic fluid substitution equations.