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Diffusion-length calculations of neutrons are performed using the Chebyshev polynomials of the second kind. The neutrons are assumed to move with constant energy in a uniform homogeneous slab. An alteative scattering keel called an Anl1-Güng?r phase function and a traditional Henyey-Greenstein phase function are used for the scattering function in the stationary neutron trans-port equation. First, analytic expressions and then numer-ical results are obtained for the diffusion length for various values of the scattering and cross-sectional parameters. Numerical results obtained from both scattering keels for the diffusion length of the neutrons are given in tables side by side for comparison.The applicability of the method is easily demonstrated by these results.