Thermal expansion of two-dimensional itinerant nearly ferromagnetic metal is investigated according to the recent theoretical development of magneto-volume effect for the three-dimensional weak ferromagnets. We particularly focus on the T-2-linear thermal expansion of magnetic origin at low temperatures, so far disregarded by conventional theories. As the effect of thermal spin fluctuations we have found that the T-linear thermal expansion coefficient shows strong enhancement by assuming the double Lorentzian form of the non-interacting dynamical susceptibility justified in the small wave-number and low frequency region. It grows faster in proportional to y(-1/2) as we approach the magnetic instability point than two-dimensional nearly antiferromagnetic metals with ln(1/y(s)) dependence, where y and y(s) are the inverses of the reduced uniform and staggered magnetic susceptibilities, respectively. Our result is consistent with the Gruneisen's relation between the thermal expansion coefficient and the specific heat at low temperatures. In 2-dimensional electron gas we find that the thermal expansion coefficient is divergent with a finite y when the higher order term of non-interacting dynamical susceptibility is taken into account.