A search for solar axions has been performed using an axion helioscope which is equipped with a 2.3m-long 4T superconducting magnet, a gas container to hold dispersion-matching gas, PIN-photodiode X-ray detectors, and a telescope mount mechanism to track the sun. A mass region around m_a = 1eV was newly explored. From the absence of any evidence, analysis sets a limit on axion-photon coupling constant to be g < 5.6-13.4x10^{-10} GeV^{-1} for the axion mass of 0.84<m_a<1.00eV at 95% confidence level. It is the first result to search for the axion in the g-m_a parameter region of the preferred axion models with a magnetic helioscope.