TT Arietis (TT Ari) is a nova-like cataclysmic variable of the VY Scl subtype, with light curve variations on multiple timescales. Besides the superhump modulation, quasi-periodic oscillations (QPOs) have been found. The aim is to determine the occurrence, strength and variability of QPOs in TT Ari, based on more complete data than in previous works. The data were obtained during the high state of TT Ari in October 2012 by the MOST space telescope, covering a total of 361.2 hours of continuous observation. We searched for frequencies over subsets of time using a Fourier-like power spectrum and then added the frequencies together forming groups. Our method has revealed QPOs that occur in 'frequency groups', which are events with a continuous oscillation of similar, constant or slowly variable frequency. We report a total of 160 frequency groups in the period range between 14 and 53 minutes (27 and 98 days^-1^), with two peaks in the power spectrum at 18.5 and 33.8 minutes (42.5 and 77.5 days^-1^). The duration of these frequency groups varies between 0.72 and 7.5 hours (average 2.8 hours) revealing between 3 and 18 complete cycles in the light curve. Most of them show significant frequency variations over the course of their duration. Sometimes two frequency groups occur simultaneously. An analysis with randomised data confirms that stochastic processes can only explain a fraction of the QPOs found. The occurrence of QPOs appears not to be related to the superhump phase.