The neutron ambient dose equivalent induced by galactic cosmic-ray-like (1 GeV/u 56 Fe) radiation stopped in a thick aluminum shield was measured at different angles with a GSI neutron ball, the standard TLD (thermoluminescent dosimeters)-based neutron dosimeter for area monitoring at the GSI facility. In order to measure reliably at large angles, a modified version of the GSI ball, including a set of three more sensitive TLD600H/700H cards, instead of one standard TLD600/700 card was used. The modified GSI balls were calibrated in neutron reference fields of 241 Am-Be(α,n) available at the Physikalisch-Technische Bundesanstalt (PTB). The neutron ambient dose equivalent was measured at five different angles (15, 40, 90, 115, and 130 degrees) with respect to the beam direction and compared to the calculated detector response and neutron ambient dose equivalent results from FLUKA simulations. The dosimeter readings were corrected for signal contributions coming from secondary charged particles. An agreement within 15% was found between the measured and calculated GSI ball response and an agreement within 30% was found between experiments and calculated neutron dose equivalents.