The discontinuous changes of volume Δ V m, entropy Δ S m and heat capacity at constant pressure Δ C P, m at the melting point have been predicted by the Landau theory of phase transition where the Gibbs free energy Φ in order state is expressed by Φ = Φ 0 + A η 2 − C η 4 + E η 6, where η is an order parameter. In this work, A is given by a function that A = k 0( T − T 0) m ( P 0 − P) n , where k 0, m, n, T 0, and P 0 are constants. The order parameter η min for the minimum of Φ min is related to the volume of solid V s and is expressed by: C A * 2 η min 4 − 3 8 C A * 3 η min 6 = 1 − Δ V Δ V m where Δ V = V s − V m, s, Δ V m = V m, l − V m, s and A * is the value of A at the melting point. The volume of V s changes from V m, s to V m, l, where Δ V m, s and Δ V m, l are volumes of solid and liquid phases at the melting point, respectively. The discontinuous change of thermal pressure coefficient γ v = (∂ P/∂ T) V , thermal expansion (∂ V/∂ T) P and compressibility −(∂ V/∂ P) T at the melting point has been calculated. A typical function of Φ for a polymer has been demonstrated as a function of η and C at the melting transition.