We consider a self-avoiding walking polymer chain with nearest-neighbor ferromagnetic Ising interaction (J>0) on the simple cubic lattice. The magnetic and conformational properties are simulated using Monte Carlo technique with bond-fluctuation model. Spontaneous magnetization is observed at low temperature. We estimate the critical temperature T-c=1.37+/-0.05(J/k(B)) and the critical exponents alphaapproximate to0.42 and nuapproximate to0.80 based on the finite-size scaling law. The values of alpha and nu are different from those of two- or three-dimensional Ising models, indicating that the phase transition in the Ising polymer chain model belongs to a different universality class. Near T-c, the chain also undergoes a collapse transition from random coil at T>T-c to compacted globule at T