  We investigate the behaviour of tensor fluctuations in Loop Quantum
Cosmology, focusing on a class of scaling solutions which admit a near
scale-invariant scalar field power spectrum. We obtain the spectral index of
the gravitational field perturbations, and find a strong blue tilt in the power
spectrum with $n_t \approx 2$. The amplitude of tensor modes are, therefore,
suppressed by many orders of magnitude on large scales compared to those
predicted by the standard inflationary scenario where $n_t \approx 0$.
