The flavour singlet structure functions of deep inelastic scattering processes can yield more decisive tests of QCD than the non-singlet. We give analytical expression for flavour singlet structure functions through analysing the lepton-nucleon deep inelastic scattering processes by means of QCD and using Jacobi polynomials. This expression contains 4 to 5 parameters and shows the changes of the singlet structure functions with x and Q2 very well. In QCD leading order, the conclusion is in reasonable agreement with experimental data.