The specific heat C as functions of temperature T and static magnetic field H in an organic molecule-based ferrimagnetism is investigated in terms of an Ising Hamiltonian for an alternating spin chain.The curves of the specific heat show double-peak structure with different parameter ratios

indicating the complex thermodynamic behavior due to the competition of the ferromagnetic interactions and antiferromagnetic interactions.Meanwhile

in the increasing magnetic fields

the sharp peak in low temperature shifts to high temperature and the Schottky-like peak in high temperature shifts to low temperature

indicating the ferromagnetic nature and antiferromagnetic nature

respectively.Compared to those of the Quantum Monte Carlo method and exact diagonalization method

the results of this paper are more precise than them.