Grob represented Switzerland in Chess Olympiads.
He also played for Switzerland in some friendly matches.
Grob played several matches.
In 1926, he tied for 10-12th in Meran (Edgar Colle won). In 1932, he tied for 9-12th in Bern (Alexander Alekhine won). In 1934, he tied for 13-14th in Zurich (Alekhine won). In 1935, he took 3rd, behind Flohr and Koltanowski, in Barcelona, took 3rd in Rosas (Flohr won), and took 10th in Bad Nauheim (Bogoljubow won). In 1936, he took 10th in Dresden (Alekhine won), tied for 3rd-4th in Reus, and took 2nd, behind Erik Lundin, in Ostend. In 1937, he tied for 1st-3rd with Reuben Fine and Paul Keres in Ostend. In 1939, he took 9th in Stuttgart (Europa Turnier; Bogoljubow won).
In 1947, he tied for 2nd-3rd, behind Savielly Tartakower in Baarn, and took 5th in Venice (Tartakower won). In 1947/48 he tied for 2nd-4th, behind László Szabó, in Hastings. In 1948, he took 8th in Venice (Miguel Najdorf won). In 1949/50 he took 4th in Lucerne (Blau won). In 1951, he took 10th in Bad Pyrmont (zonal; Svetozar Gligorić won).
Between 1946 and 1972, Grob played 3,614 correspondence chess games. He won 2,703, lost 430, and drew 481 games. All of the games were played against readers of the Neue Zürcher Zeitung, a leading Swiss newspaper.
He was awarded the IM title in 1950.