Grob represented Switzerland in Chess Olympiads.
- In 1927, at fourth board in 1st Chess Olympiad in London (+2 –5 =7);
- In 1935, at second board in 6th Chess Olympiad in Warsaw (+2 –8 =5);
- In 1936, at third board in 3rd unofficial Chess Olympiad in Munich (+4 –7 =6);
- In 1952, at first board in 10th Chess Olympiad in Helsinki (+6 –6 =1).
He also played for Switzerland in some friendly matches.
- In 1950, he lost to Carlos Guimard 0,5 : 1,5 in Zurich (SUI – ARG);
- In 1951, he drew with Eugenio Szabados 1 : 1 in Venice (SUI – ITA);
- In 1952, he drew with Rudolf Teschner 1 : 1 in Lucerne (SUI – FRG);
- In 1955, he won against Weichselbaumer 1 : 0 in Zurich (SUI – Saar).
Grob played several matches.
- In 1933, he lost to Salo Flohr (+1 –4 =1)
- In 1934, he won against Jacques Mieses (+4 –1 =1)
- In 1935, he lost to Lajos Steiner (+1 –3 =0)
- In 1937, he drew with George Koltanowski (+1 –1 =2)
- In 1947, he lost to Max Euwe (+0 –5 =1)
- In 1948, he lost to Miguel Najdorf (+1 –5 =0)
- In 1949, he lost to Efim Bogoljubow (+2 –4 =1)
- In 1950, he lost to Lodewijk Prins (+1 –4 =1).
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 Zürich 1934 (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 International Master title in 1950.
Grob married nine times. When once asked if he were married he replied "Fast immer" ("Almost always.")
- Salomon Flohr vs Henri Grob, Match 1933, Queen Pawn Game: Krause Variation (D02), 0-1
- Henri Grob vs Aron Nimzowitsch, Zurich 1934, Alekhine Defense: Normal Variation (B03), ½–½
- '3 July' according to Gaige, '8 July' according to Golombek, '4 June' according to Mundo del Ajedrez November 1974, p. 318.
- OlimpBase :: the encyclopaedia of team chess
- Litmanowicz, Władysław & Giżycki, Jerzy (1986, 1987). Szachy od A do Z. Wydawnictwo Sport i Turystyka Warszawa. ISBN 83-217-2481-7 (1. A-M), ISBN 83-217-2745-X (2. N-Z)