A hybrid system for a vehicle including a hybrid machine and a transmission arrangement that includes a first, a second and a third planetary gear set each including a sun gear, a planet carrier and a ring gear, the transmission arrangement further including five shift elements engageable in combinations of two to obtain six forward gear stages, wherein the ring gear of the first planetary gear set and the planet carrier of the second planetary gear set are operatively connected to each other, the ring gear of the second planetary gear set and the planet carrier of the third planetary gear set are operatively connected to each other, two planetary members of the third planetary gear set are selectively connectable to each other by a single one of the shift elements, wherein the hybrid machine and the ring gear of the first planetary gear set are connected to each other.