In this research, we investigate electron cyclotron resonance heating (ECRH) for low-energy electrons analytically and numerically, which is applicable to ECRH-assisted plasma start-up in a tokamak. From the previous experimental studies, it is well known that the first harmonic ECRH is more effective than the second harmonic ECRH. In this work, we develop an analytic model of ECRH in the start-up process and present comparisons of efficiency between the first harmonic and the second harmonic. It is found that electrons gain a large amount of energy from the waves at the first harmonic resonance up to several hundred electronvolts. However, electrons gain a large amount of energy from the waves only up to ∼10 eV and the energy gain starts decreasing afterwards at the second harmonic resonance. When seed electrons are heated from room temperature to a temperature far above the ionization energy, the seed electrons can bring about an avalanche of electrons. Thus, pre-ionization with the second harmonic can be delayed since electrons need more time to be heated up to the breakdown temperature due to the slow heating speed compared with the first harmonic ECRH.