The logging-while-drilling (LWD) quadrupole wave is a dispersive wave mode guided along the borehole with a drill collar. The wave is sensitive to the formation alteration caused by drilling. We inverted LWD quadrupole-wave dispersion data to estimate a radial shear-velocity profile away from the wellbore. We also explored the nonuniqueness of the inverse problem and solved it by using a constrained inversion method. This was done by constraining the high-frequency portion of the model dispersion curve with another curve calculated using the near-borehole velocity. The constraint condition is based on the physical principle that a high-frequency LWD quadrupole wave has a shallow penetration depth and is therefore sensitive to the near-borehole shear velocity. Particularly, we found that a monotonically continuous velocity profile can be well approximated using a one-zone equivalent model, allowing for a drastic simplification of the inversion process. We used theoretical modeling and real data examples to validate the method for the LWD wave data. The quadrupole dispersion data and the inversion results clearly demonstrated that formation alteration can occur even while the well is being drilled.