The Lagrangian dispserion of fluid particles in inhomogeneous turbulence is investigated by a direct numerical simulation of turbulent channel flow. Fluid particle velocity and acceleration along a particle trajectory are computed by employing several interpolation schemes such as linear interpolation, high-order Lagrange polynomial interpolation and the Hermite interpolation schemes. The performances of the schemes are evaluated through comparison of errors in computed particle positions, velocities and accelerations against spectral interpolation. Adopting the four-point Hermite interpolation in the homogeneous directions and Chebyshev polynomials in the wall-normal direction appears to produce most reliable Lagrangian statistics including acceleration correlations with a reasonable amount of computational overhead.