Seismic-wave anisotropy has long been an important topic in the exploration and development of unconventional reservoirs, especially in shales, which are commonly characterized as transversely isotropic ([TI] or vertical TI [VTI]) media. At present, the shear-wave (S-wave) TI properties have mainly been determined from monopole Stoneley- or dipole flexural-wave measurements in wireline acoustic logging, but the feasibility of those obtained from logging-while-drilling (LWD) acoustic data needs to be established. We have developed a joint inversion method for simultaneously determining formation S-wave transverse isotropy and vertical velocity from LWD multipole acoustic data. Our theoretical analysis shows that the presence of anisotropy strongly influences LWD Stoneley- and quadrupole-wave dispersion characteristics. Although the monopole Stoneley and quadrupole waves are sensitive to the formation S-wave TI parameters, they suffer from the typical nonuniqueness problem when using the individual-wave data to invert parameters alone. Thus, the respective dispersion data can be jointly used to estimate the formation S-wave TI properties. By the joint inversion, the nonuniqueness problem in the parameter inversion can also be effectively alleviated. The feasibility of the method has been verified by the processing results of theoretical synthetic data and field LWD acoustic-wave data. Therefore, the result offers an effective method for evaluating VTI formation anisotropy from acoustic LWD data.