Photoelectric current is related to how many electrons are ejected, not to their maximum velocity. When you shine a beam of photons on a metal, it is likely that each photon will hit only one electron. In the process, it will transfer all its energy to the electron. This energy is given by E=hf. f is the frequency. or E=hc/L. where L is the wavelength. If this energy is greater than the work function Phi and the electron is on the surface of the metal then it will be ejected.The work function is the minimum energy required to eject a photoelectron i.e. the energy required to eject an electron from the surface. The difference between the work function and the photon energy will give you the max kinetic energy that the photoelectron can have (and thus it's max velocity). Notice that in our discussion to determine the highest velocity we only needed the work function (a constant for every metal) and the photon energy. Photoelectric current, on the other hand, is related to the NUMBER of photoelectrons ejected. If the above story repeats many times, i.e. there are many photons striking many electrons and causing them to be ejected then a higher current will be produced. Note that the current is related to the number of photons striking the metal that have energies greater than the work function. The more photons of this type that you have the more electrons will be ejected and the higher the photoelectric current. Now intensity comes into play. Intensity is the energy transferred per unit area per unit time. So if you have only one type of photons (i mean photons of only one frequency) then to increase the intensity you have to increase the number of photons. ( The other way to increase intensity is to increase the frequency of photons making them carry more energy but this is irrelevant to our discussion since it will increase the max velocity not the current). If you increase the number of photons you will thus get a higher photoelectric current but with the same max velocity.
I hope that helped.
