We present a new inverse scattering series for quantum elastic scattering in three spherical dimensions. The new series, which converges absolutely, independent of the strength of the scattering interaction, results from a renormalization transformation of the Lippmann-Schwinger Fredholm integral equation to a Volterra form. A new feature of the formulation is that it does not require the determination of phase shifts and it can be applied even to integral cross-section measurements. The approach is illustrated by application to a simple example problem.