We report the results of the analysis of an AstroSat observation of the Black Hole candidate MAXI J1535 - 571 during its Hard Intermediate state . We studied the evolution of the spectral and timing parameters of the source during the observation . The observation covered a period of \sim 5 days and consisted of 66 continuous segments , corresponding to individual spacecraft orbits . Each segment was analysed independently . The source count rate increased roughly linearly by \sim 30 % . We modelled the spectra as a combination of radiation from a thermal disk component and a power-law . The timing analysis revealed the presence of strong Quasi Periodic Oscillations with centroid frequency \nu _ { QPO } fluctuating in the range 1.7–3.0 Hz . We found a tight correlation between the QPO centroid frequency \nu _ { QPO } and the power-law spectral index \Gamma , while \nu _ { QPO } appeared not to be correlated with the linearly-increasing flux itself . We discuss the implications of these results on physical models of accretion .