Provided are a cascaded photovoltaic grid-connected inverter, a control method and a control device for the same. The method includes: determining whether at least one of inverter units of the cascaded photovoltaic grid-connected inverter is over-modulated; injecting a reactive current to a power grid to make a grid-connected current effective value greater than or equal to √{square root over (2)}*idcmin, in a case that at least one of the inverter units is over-modulated; determining a voltage U0 required for grid connection for the cascaded photovoltaic grid-connected inverter corresponding to a current grid-connected current effective value; and adjusting an output active voltage of each of the inverter units according to Ujd=Pj/P0*U0d, and adjusting an output reactive voltage of each of the inverter units in a case that none of the inverter units is over-modulated.