The high-l Rydberg Stark states are populated by the state transfer from initial prepared nS Rydberg state via avoided crossings induced by a weak electric-field pulse, and investigated by the state selective field ionization method in a cesium standard magneto-optical trap. The dependences of the transfer rate, given by the ratio of the number of high-l Stark states to all atoms, on the strength and holding time of electric-field pulse are investigated and compared with those with additional ions. The results show that the time evolution of high-l Stark states strongly depends on the electric-field strength, and is affected by the additional ions at relatively weaker field (1.51 V/cm here). The density of Rydberg atoms has a minor effect on the characteristic time of evolution process.