In one aspect, a system for adjusting closing disc penetration depth of a seed-planting implement may include a furrow closing assembly having at least one closing disc configured to penetrate the soil in a manner that closes a furrow formed in the soil by the seed-planting implement. The system may also include an actuator configured to adjust a penetration depth of the at least one closing disc. Furthermore, the system may include a controller configured to receive an input indicative of at least one of an operation of the seed-planting implement or a field condition of a field across which the seed-planting implement is being moved. Additionally, the controller may be further configured to control an operation of the actuator in a manner that adjusts the penetration depth of the at least one closing disc based on the received input.