This paper investigates the design of practical non-binary irregular repeat-accumulate (IRA) codes for reliable physical-layer network coding. In the scheme, a same random-coset IRA code over Galois field GF(q) is employed at the two users. The relay computes the network coded message sequence directly from the superimposed signal using an iterative belief propagation algorithm. We explore the symmetry and permutation-invariant properties of the decoder's soft information distribution and adopt a two-dimension extrinsic information transfer chart to analyze and optimize the coding scheme. Numerical results demonstrate that our developed scheme achieves near-capacity performance in Gaussian two-way relay channels.