The criticality problem is studied based on one-speed time-dependent neutron transport theory, for a uniform and finite slab, using the Marshak boundary condition. The time-dependent neutron transport equation is reduced to a stationary equation. The variation of the critical thickness of the time-dependent system is investigated by using the linear anisotropic scattering kernel together with the combination of forward and backward scattering. Numerical calculations for various combinations of the scattering parameters and selected values of the time decay constant and the reflection coefficient are performed by using the Chebyshev polynomials approximation method. The results are compared with those previously obtained by other methods which are available in the literature. (C) 2009 Elsevier Ltd. All rights reserved.