We have investigated the low-lying energy spectrum and electromagnetic transition strengths in even-even $^{76}$Se using the proton-neutron interacting boson model (IBM-2). The theoretical calculation for the energy levels and $E2$ and $M1$ transition strengths is in good agreement with the experimental data. Especially, the excitation energy and $E2$ transition of $0^+_2$ state, which is intimately associated with shape coexistence, can be well reproduced. The analysis on low-lying states and some key structure indicators indicates that there is a coexistence between spherical shape and $\gamma$-soft shape in $^{76}$Se.