Goldman was born in Neupest, a suburb of Budapest, Hungary. His father, Rabbi Yosef Goldman, was the chief rabbi and Av Beit Din of the Orthodox Jewish community. In 1926, at the age of 21, Goldman became a rabbi in Romania, and in 1934 in Bessarabia (then part of Romania). In 1938, after his father died, he was given his father's position as chief rabbi and Av Beit Din of the Orthodox Jewish community in Neupest.
To save his family from the 1944 Nazi invasion of Hungary—which he anticipated just in time—Goldman obtained false papers that certified them as Aryans. After the war, Goldman's family lived in Hamburg, Germany. During his time in Germany, Goldman involved himself in Vaad Hatzalah activities. The Joint Distribution Committee arranged for their emigration to the United States, and in April 1949, Goldman was able to reach America's shore aboard the Marine Shark.
In the United States, Goldman was a dayan and publisher of seforim. He published a Shas and various other seforim. His Shas was one of the most popular editions available at the time. Initially, Goldman lived on the Lower East Side, Manhattan, then in Crown Heights, Brooklyn, and finally in Boro Park, Brooklyn. In Boro Park, he served as rabbi of a synagogue known as "Naipest" (namesake of his previous rabbinate, in Hungary). He died in Boro Park in 1980.