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We study the geometric phase of a qutrit-qubit mixed-spin system in an exteal homogeneous magnetic field.Both the spin-spin interaction strength J and the exteal magnetic field B can affect the geometric phase of the system.In addition,we consider the negativity of the composite system.The relationship between the negativity and the geometric phase is obtained.Finally,we calculate the geometric phase for a thermal mixed state and show how the geometric phase depends on the resealed coupling parameter and temperature.In the limit T→0,we can recover the result of the ground state.This analysis has some implications in realistic implementations of geometric quantum computation.