Using the numerical diagonalization method, we investigate the ferromagnetism and the superconductivity in the multi-orbital Hubbard model in one-dimension. To examine the superconductivity, we calculate the critical exponent K-p, based on the Luttinger liquid theory and the anomalous flux quantization in the superconducting region. Analyzing the value of K-p, we obtain the phase diagram on the U '-J parameter plane including the superconducting phase and the fully polarized ferromagnetic phase. (c) 2006 Elsevier B.V. All rights reserved.