Negative parity energy states in 121–131 La have been studied using Projected Shell Model (PSM). Some nuclear structure properties like yrast spectra, back-bending in moment of inertia, reduced transition probabilities and band diagrams have been described. The experimental feature of the co-existence of prolate–oblate shapes in 125–131 La isotopes has been satisfactorily explained by PSM results. Comparison of the theoretical data with their experimental counterparts has also been made. From the calculations, it is found that the yrast states arise because of multi-quasiparticle states.