Deep-sea mining vehicle for taking up mineral deposits from a seabed at great depth, wherein the vehicle comprises a support frame provided with means for moving the vehicle forward on the seabed in a direction of movement, with a storage for the mineral deposits taken up, and further with at least one suction head with an open suction side which is directed toward the seabed and is provided in a suction plane, and along which the mineral deposits are taken up, wherein a width direction of the at least one suction head coincides with a width direction of the deep-sea mining vehicle, wherein the deep-sea mining vehicle is further provided with a control device for keeping the height of the suction plane within predetermined limits relative to the seabed, wherein the control device comprises measuring means for obtaining seabed heights at positions which precede the open suction side relative to the direction of movement and which extend over a width of the deep-sea mining vehicle, and further comprises an actuator which is incorporated in a control circuit and which is configured on the basis of the seabed heights measured at the positions to adjust the height of the suction plane of the at least one suction head such that it remains between the predetermined limits relative to the seabed, and wherein the measuring means comprise an elongate carrier which precedes the open suction side relative to the direction of movement, wherein the carrier is provided with a series of sources configured to generate a geophysical signal under water in the direction of the seabed, and with a series of receivers configured to measure a response signal returning via the seabed, wherein the carrier extends in the width direction of the deep-sea mining vehicle over a width of the deep-sea mining vehicle, wherein the at least one suction head has a width, characterised in that the seabed heights measured in the width direction of the deep sea mining vehicle are filtered of outlying values, a subset of seabed heights over the width of the at least one suction head is determined, and a maximum seabed height over the width of the at least one suction head is calculated from the subset, wherein the actuator is configured on the basis of the calculated maximum seabed height to adjust the height of the suction plane of the at least one suction head such that it remains between the predetermined limits relative to the seabed. wherein the vehicle comprises a support frame provided with means for moving the vehicle forward on the seabed in a direction of movement, with a storage for the mineral deposits taken up, and further with at least one suction head with an open suction side which is directed toward the seabed and is provided in a suction plane, and along which the mineral deposits are taken up, wherein a width direction of the at least one suction head coincides with a width direction of the deep-sea mining vehicle, wherein the deep-sea mining vehicle is further provided with a control device for keeping the height of the suction plane within predetermined limits relative to the seabed, wherein the control device comprises measuring means for obtaining seabed heights at positions which precede the open suction side relative to the direction of movement and which extend over a width of the deep-sea mining vehicle, and further comprises an actuator which is incorporated in a control circuit and which is configured on the basis of the seabed heights measured at the positions to adjust the height of the suction plane of the at least one suction head such that it remains between the predetermined limits relative to the seabed, and wherein the measuring means comprise an elongate carrier which precedes the open suction side relative to the direction of movement, wherein the carrier is provided with a series of sources configured to generate a geophysical signal under water in the direction of the seabed, and with a series of receivers configured to measure a response signal returning via the seabed, wherein the carrier extends in the width direction of the deep-sea mining vehicle over a width of the deep-sea mining vehicle, wherein the at least one suction head has a width, characterised in that the seabed heights measured in the width direction of the deep sea mining vehicle are filtered of outlying values, a subset of seabed heights over the width of the at least one suction head is determined, and a maximum seabed height over the width of the at least one suction head is calculated from the subset, wherein the actuator is configured on the basis of the calculated maximum seabed height to adjust the height of the suction plane of the at least one suction head such that it remains between the predetermined limits relative to the seabed.