An improved test of time dilation in special relativity has been performed using laser spectroscopy on fast ions at the heavy-ion storage-ring TSR in Heidelberg. The Doppler-shifted frequencies of a two-level transition in 7Li+ ions at v = 0.064c have been measured in the forward and backward direction to an accuracy of /= 1x10--9 using collinear saturation spectroscopy. The result confirms the relativistic Doppler formula and sets a new limit of 2.2x10--7 for deviations from the time dilation factor SR = (1--v2/c2)--1/2.