We analyze the polarization properties of photons which are produced in the unpolarized b-quark decay, b --> syg. Using the structure function formalism we carry out a general analysis of the polarization characteristics of y in terms of the standard Stokes parameters. The expressions for five independent structure functions are constructed in terms of the weak magnetic transition form factors of the vertices b -->, sy and b --> sg. Numerical calculations of the Stokes parameters and various differential distributions for b --> syg are performed for the two-Higgs doublet model (2HDM). We studied the dependences of all these characteristics to the model parameters. These results were compared with the Standard Model predictions for different top quark masses. Strong sensitivity of the Stokes parameters, which defines the linear photon polarization, to the model is demonstrated.