The purpose of the present work is to study the negative parity yrast bands in odd-mass 101−109Cd nuclei in the framework of Projected Shell Model (PSM). The results are obtained for the energy spectrum, reduced transition probabilities [ B ( E 2 ) ], rotational alignment etc. The yrast and excited band spectra of these isotopes are found to arise from the quasiparticle states around the Fermi level. The yrast and excited band spectra are found to depend sensitively on the different single particle and multi-quasiparticle configurations at low- and high-spins respectively. This work also substantiates the observed presence of anti-magnetic rotation in 105,107,109Cd nuclei.