Phase diagram and critical phenomena of a frustrated Blume-Capel model with alternating single-ion anisotropy ± D, nearest- and next-nearest-neighbour exchange interactions with equal magnitude J are studied by the Monte Carlo simulations using Wang-Landau sampling and nonequilibrium relaxation method. The collinear ordered phase due to next-nearest-neighbour interaction and partial ordered phase due to alternating anisotropy are confirmed together with a paramagnetic phase. We obtained the numerical results which strongly suggests that a single phase transition at D = 0 splits into two Ising lines as soon as D is switched on. With the increase of D, the critical point of the easy-axis sublattice stays on a usual Ising-like critical line while that of the easy-plane sublattice passes through the tricritical point and the transition becomes of the first order as in the usual Blume-Capel model. © 2010.