Phase transition of a self-avoiding walking polymer chain with spatial nearest neighbor ferromagnetic Ising interaction on the simple cubic lattice is investigated using Metropolis dynamic Monte Carlo technique. Magnetic susceptibility x is determined from the Brillouin function and from the linear response of magnetization to external magnetic field in small field region. We find the later is better, though both are in consistent with each other at high temperatures. The magnetic susceptibility X can be expressed using the Curie law and thus the Curie temperature theta is estimated. The chain length dependent Curie temperature theta of the chain model can be well fitted as theta = 1.40 - 4.0 xn(-0.619) based on the finite-size scaling law. The transition temperature for an infinite long chain theta(infinity) = 1.40J/k(B), and the exponent b = 0.619 are in agreement with our previous study.