Asa Porter Grover (February 18, 1819 – July 20, 1887) was a United States representative from Kentucky.

He was born near Phelps, New York where he attended the common schools before moving to Kentucky in 1837.

He attended Centre College in Danville, Kentucky and taught school in Woodford and Franklin Counties.

In addition, he studied law and was admitted to the bar in 1843 and commenced practice in Owenton, Kentucky.

He moved to Georgetown, Kentucky in 1881 and continued the practice of law until his death in that city on July 20, 1887.