High-spin states of (84)Sr are populated through the reaction (70)Zn ((18)O, 4n) (84)Sr at the beam energy of 75 MeV. The measurements of excitation functions, γ-γ coincidences, directional correlations of oriented states (DCO) ratios and γ-transition intensities are performed using eight anticompton HPGe detectors and one planar HPGe detector. Based on the experimental results, we establish a new level scheme of (84)Sr, in which 12 new states and nearly 30 new γ-transitions are identified in the present work. The positive-parity yrast band is extended to spin I(π) = 24(+), while one negative-parity band is extended to spin I(π) = 19(-) and it is found that the even-spin and odd-spin members in high-spin states show the nature of signature staggering. The deformation of (84)Sr is studied by calculating the total-Routhian-surfaces (TRS) of positive-parity yrast states in the cranked shell model formalism.