The static critical exponents of the three-dimensional Blume-Capel model which has a tricritical point at D/J = 2.82 value are estimated for the standard and the cooling algorithms which improved from Creutz cellular automaton. The analyses of the data using the finite-size scaling and power-law relations reproduce their well-established values in the D/J < 3 and D/J < 2.8 parameter region at standard and cooling algorithms, respectively. For the cooling algorithm at D/J = 2.8 value of single-ion anisotropy parameter, the static critical exponents are estimated as beta = 0.31, gamma = gamma' = 1.6, alpha = alpha' = 0.32 and nu = 0.87. These values are different from beta = 0.31, gamma = gamma' = 1.25, alpha = alpha' = 0.12 and nu = 0.64 universal values. This case indicated that the BC model exhibits an ununiversal critical behavior at the D/J = 2.8 parameter value near the tricritical point (D/J = 2.82). The simulations were carried out on a simple cubic lattice with periodic boundary conditions. (c) 2005 Elsevier B.V. All rights reserved.