We report on the detection of X-ray emission from the supernova remnant (SNR) G359.1-0.5 in a deep ROSAT PSPC pointed observation. The diffuse emission is well confined within the radio shell of the SNR. Its spectrum can be represented by a thermal plasma model at T∼1 keV and F_x∼2×10⁻¹¹ erg cm⁻² s⁻¹ (0.1–2.0 keV) modified by the column absorption of N_H∼3×10²² cm⁻². This result supports the view that the source is at a large distance consistent with that from radio observation, and helps to resolve a puzzle about the SNR in previous observations.