Electrons can be accelerated to a GeV level in centimeters by plasma wakefield driven by laser. With the development of chirped pulse amplification technique, the accelerating field can reach 100 GV/m. The laser driven wakefield acceleration experiments with ionization injection are carried out using 68 TW (1.7 J, 25 fs) laser and a mixture gas of 99% He and 1% N2. In experiment, the output electron beam has broadband spectrum with a maximum cut-off energy of about 290 MeV and a maximum output energy is quite stable in a certain range of laser focal positions. Two-dimensional particle-in-cell simulation is carried out. It is found that the longitudinal phase space is occupied by the continuously injected electrons and the phase space distribution is quite stable after the laser has propagated several millimeters inside plasma. This acceleration process can lead to quite stable maximum output energy of electron beam. These experiments reveal the physical nature of continuous ionization injection, which is very important for improving the performance of ionization injection.