The parent of Costa Mesa-based Hyundai Motor America Inc. is recalling 13,500 of its Veloster models due to an installation problem with the coupe’s sunroof that could cause its glass to shatter.

The recall affects model year 2012 Velosters made between Nov. 1, 2011 and April 17, 2012, according to a National Highway Traffic Safety Administration document.

The recall will begin in January.

The NHTSA received 11 complaints related to the sunroof, triggering an evaluation in October.

Hyundai told the NHTSA that it had received 76 warranty claims, 20 complaints and six field reports related to the sunroof problem and that there were five reports of minor cuts caused.

In a separate NHTSA filing, Hyundai is also recalling manual transmission Velosters for a parking-brake problem.

The recall affects 4,490 model year 2012 Velosters made between July 2, 2011 and Feb. 27, 2012.

Veloster 2012 sales through November totaled 32,886.