Spectroscopy and V,I CCD photometry of the dwarf irregular galaxy SBS 1129+576 are presented for the first time . The CCD images reveal a chain of compact H ii regions within the elongated low-surface-brightness ( LSB ) component of the galaxy . Star formation takes place mainly in two high-surface-brightness H ii regions . The mean ( V - I ) colour of the LSB component in the surface brightness interval \mu _ { V } between 23 and 26 mag arcsec ^ { -2 } is relatively blue \sim 0.56 \pm 0.03 mag , as compared to the ( V - I ) \sim 0.9 – 1.0 for the majority of known dwarf irregular and blue compact dwarf ( BCD ) galaxies . Spectroscopy shows that the galaxy is among the most metal-deficient galaxies with an oxygen abundance 12 + log ( O/H ) = 7.36 \pm 0.10 in the brightest H ii region and 7.48 \pm 0.12 in the second brightest H ii region , or 1/36 and 1/28 of the solar value 12+log ( O/H ) _ { \odot } = 8.92 ( Anders & Grevesse [ ] ) . , respectively . H \beta and H \alpha emission lines and H \delta and H \gamma absorption lines are detected in a large part of the LSB component . We use two extinction-insensitive methods based on the equivalent widths of ( 1 ) emission and ( 2 ) absorption Balmer lines to put constraints on the age of the stellar populations in the galaxy . In addition , we use two extinction-dependent methods based on ( 3 ) the spectral energy distribution ( SED ) and ( 4 ) the ( V - I ) colour . Several scenarios of star formation were explored using all 4 methods . The observed properties of the LSB component can be reproduced by a stellar population forming continuously since 10 Gyr ago , provided that the star formation rate has increased during the last 100 Myr by a factor of 6 to 50 and no extinction is present . However , the observational properties of the LSB component in SBS 1129+576 can be reproduced equally well by continuous star formation which started not earlier than 100 Myr ago and stopped at 5 Myr , if some extinction is assumed . Hence , the ground-based spectroscopic and photometric observations are not sufficient for distinguishing between a young and an old age for SBS 1129+576 .