  In this work, we develop the shadow formalism for two-dimensional Galilean
conformal field theory (GCFT$_2$). We define the principal series
representation of Galilean conformal symmetry group and find its relation with
the Wigner classification, then we determine the shadow transform of local
operators. Using this formalism we derive the OPE blocks, Clebsch-Gordan
kernels, conformal blocks and conformal partial waves. A new feature is that
the conformal block admits additional branch points, which would destroy the
convergence of OPE for certain parameters. We establish another inversion
formula different from the previous one, but get the same result when
decomposing the four-point functions in the mean field theory (MFT). We also
construct a continuous series of bilocal actions of MFT, and an exceptional
series of local actions, one of which is the BMS free scalar model. We notice
that there is an outer automorphism of the Galilean conformal symmetry, and the
GCFT$_2$ can be regarded as null defect in higher dimensional CFTs.
