Spin-spin correlation function and temperature dependence of magnetic susceptibility were calculated for the finite-size Hamiltonian of an S = 1 and S = 1/2 antiferromagnetic Heisenberg chain. The S = 1 site in the chain is composed of two S = 1/2 spins coupled by finite ferromagnetic interaction. This is the simplest model Hamiltonian for organic molecule-based ferrimagnetics consisting of two kinds of molecules with different spin quantum numbers. The Hamiltonian possesses a magnetic degree of freedom in the S = 1 site and a multicentered nature of the intermolecular interactions, both of which are essential features of molecular magnetics. The low-temperature limit of susceptibility calculated by a quantum Monte Carlo simulation method was found to obey the Curie law of S = N/2 N(1-1/2) (N: the number of repeating units), indicating that the ground state of the chain is ferrimagnetic. A quasi-exponential decay, however, was found in the groundstate correlation function calculated from the numerical diagonalization of the Hamiltonian matrix, which implies that the ground state has no long-range order at the critical point of zero-temperature.