  The finite-size scaling (FSS) theory for continuous phase transitions has
been useful in determining the critical behavior from the size dependent
behaviors of thermodynamic quantities. When the phase transition is
discontinuous, however, FSS approach has not been well established yet. Here,
we develop a FSS theory for the explosive percolation transition arising in the
Erd\H{o}s and R\'enyi model under the Achlioptas process. A scaling function is
derived based on the observed fact that the derivative of the curve of the
order parameter at the critical point $t_c$ diverges with system size in a
power-law manner, which is different from the conventional one based on the
divergence of the correlation length at $t_c$. We show that the susceptibility
is also described in the same scaling form. Numerical simulation data for
different system sizes are well collapsed on the respective scaling functions.
