The electromagnetic surface waves which propagate along a non-magnetized cold plasma column have a great value in the application of plasma antenna. In this paper, the dispersion properties, the transmission power distributions, and the radiation patterns for these electromagnetic surface waves which have lower frequencies than the electron plasma frequency are analyzed numerically. Based on Helmholtz equation, the specific expression of dispersion equation is derivedby the field matching method, then the exact values of complex axial wave vector kz under different wave frequencies are obtained by solving the transcendental dispersion relation. Using the specific value of kz obtained above, the exact expressions of transmission power profile in the plasma column and field profiles in the three regions, i.e., plasma, dielectric, and free space are derived, respectively. Finally, based on the complex form of electric conductivity that is derived from the Boltzmann-Vlasov equation with Krook term and the complex axial wave vector kz obtained above, the influence of the parameter pea/c on phase property, and the dependence of radiation pattern and transmission power profile on wave frequency of the non-magnetized cold plasma column in a cylindrical dielectric tube system are analyzed. The results show that the electron plasma frequency has a significant influence on the phase property, which is evidently confirmed by the fact that the propagation velocities of the three modes m=0, m=1 and m=2 are all near to the light speed when the value of parameter pea/c gradually increases. Meanwhile, through the investigation of the radiation patterns for the three modes, an important conclusion is that the radiation pattern has evident dependence on wave frequency. While the radiation direction of the main lobe is in the axial direction for the m=1 mode, the m1 modes each have an angle between the radiation direction of the main lobe and the axial direction, this crucial conclusion is in good agreement with the theoretical calculation results obtained from other researcher. Further, we find that with the increase of wave frequency, the angle between the main lobe radiation direction and the axial direction turns smaller for each of m=0 and m=2 modes, and the width of main lobe gradually narrows for each of all modes, and the amplitude of the first side lobe becomes notable for each of m=0 and m=2 modes and ignorable for the m=1 mode. Also, the transmission power increases as the wave frequency increases for each of all modes. These theoretical calculation results provide a detailed theoretical reference for the designing of plasma stealth and high-precision requirements of plasma antenna design, and giving a comprehensive optimization guidance for the modulation of plasma antenna.