  Galilean $W_3$ vertex operator algebra $\mathcal GW_3(c_L,c_M)$ is
constructed as a universal enveloping vertex algebra of certain non-linear Lie
conformal algebra. It is proved that this algebra is simple by using
determinant formula of the vacuum module. Reducibility criterion for Verma
modules is given, and the existence of subsingular vectors demonstrated. Free
field realisation of $\mathcal GW_3(c_L,c_M)$ and its highest weight modules is
obtained within a rank 4 lattice VOA.
