We propose a scheme for producing entangled spin-squeezed states of an atomic ensemble inside an optical cavity by backaction of a detuned quantum-nondemolition (QND) measurement. By illuminating the atoms with bichromatic light, an interaction Hamiltonian of the cross-Kerr effect between the cavity and atoms is generated to implement QND measurements. The feedback effect is obtained through mixing the phase and amplitude quadratures of the cavity field, due to the detuning of the optical cavity. Therefore the continuous nondemolition measurements are fed back to correct the quantum state of the atomic sample such that unconditional spin squeezing is produced without requiring the use of any external electronics.