TAIPEI—HTC Corp. said Thursday its unaudited third-quarter net profit grew 68%, as the Taiwan-based handset maker's smartphones continued to woo consumers away from traditional cell phones.

The Taoyuan-based company has increased market share in the U.S., Asia and Europe in recent years with its early adoption of Google Inc.'s Android software, becoming the fifth-largest producer of smartphones globally by shipments in the second quarter. Over the past year it has acquired a variety of companies, including Beats, a headphone...