The Blume-Capel model in the presence of exteal magnetic field H has been simulated using a cellular automaton algorithm improved from the Creutz cellular automaton in three-dimension lattice. The field critical exponent δ is estimated using the power law relations and the finite size scaling functions for the magnetization and the susceptibility in the range -0.1≤h=H/J≤0. The estimated value of the field critical exponent δ is in good agreement with the universal value (δ=5) in three dimensions. The simulations are carried out on a simple cubic lattice under periodic boundary conditions.