Lifetimes of excited nuclear states in 187Hg have been measured using the 159Tb (32S, p3n)187Hg reaction at a beam energy of 154 MeV at the Inter University Accelerator Center, Delhi. In the experiment, the lifetimes of the five lowest yrast states have been determined using the recoil distance Doppler-shift (RDM) method. The extracted transition quadrupole moments show a sharp increase with increasing level spin, indicating a major shape transition happening in this nucleus. For a better insight into the predicted shape coexistence picture in 187Hg nucleus, the experimental results are compared with the results of the total Routhian surface calculations. The results indicate the shifting of deformed structures from weakly prolate at low-spins to strongly prolate at high spins in 187Hg nucleus.