The Sivers effect describes the correlation between the spin of the nucleon and the orbital motion of partons. It can be measured via Semi-Inclusive Deep Inelastic Scattering of lepton on a transversely polarised proton and deuteron targets by determining the azimuthal asymmetry related to the modulation in the Sivers angle ϕSiv. In the paper a method of obtaining the Sivers asymmetry for gluons is presented. It is based on the model of lepton nucleon interactions via three single-photon-exchange processes: photon-gluon fusion (PGF), QCD Compton (QCDC) and leading process (LP). A method of simultaneous extraction of the Sivers asymmetries of the three processes with the use of Monte Carlo (MC) and neural networks (NN) approach is presented. The method has been applied to COMPASS data taken with 160GeV/c muon beam scattered off transversely polarised deuteron and transversely polarised proton target. For each target a data sample of events containing at least two hadrons with large transverse momentum has been selected. Finally the results for gluon Sivers asymmetry were obtained to be: Adg = −0.14 ± 0.15(stat.) ± 0.06(syst.) at 〈xg〉 = 0.13 and Apg = −0.26 ± 0.09(stat.) ± 0.08(syst.) at 〈xg〉 = 0.15.