What we reported Construction began on a 52.8-mile stretch of road that will extend the Grand Parkway from Hwy. 59 in New Caney to Hwy. 146 in Baytown in August. The project is slated to cost $1.28 billion and is expected to be completed in 2022. After the roadway opens, drivers will be able to take the Grand Parkway continuously from Hwy. 146 in Baytown around Houston to Hwy. 59 in Fort Bend County. The latest Construction is underway on Segment H near Hwy. 59 in New Caney and on Segment I-2B in Baytown. According to Grand Parkway Infrastructure—which is building the roadway—construction is slated to begin on the remaining segments—I-1 and I-2A—in 2019. Segment I-1 begins at I-90 east of Huffman, and I-2A begins at I-10 in Mont Belvieu.