He studied at Herlufsholm, Copenhagen, Leyden, and Franeker; became rector of Herlufsholm academy 1608; professor pædagogicus, University of Copenhagen, 1610; professor of Greek 1613; member of the theological faculty 1615. In 1617 he was appointed teacher to Prince Christian, son of King Christian IV., but returned to the university three years later. At this time Denmark was disturbed by Roman Catholic propaganda from the scholastic revival, and Brochmand made the controversy with Rome a subject of his public lectures. In 1626–28 he published his Controversiæ sacræ (3 parts), a reply in the style of Lutheran scholasticism to Cardinal Bellarmine's attacks on the Lutheran Church, and in 1634, at the king's order, he engaged in a polemic with the Jesuits, who endeavored to defend the conversion of Margrave Christian William of Brandenburg to Catholicism. In their final reply the Jesuits stigmatized Brochmand as a "disturber of the Roman empire, the boldest despiser of His Imperial Majesty and the Catholic rulers, a poisonous spider, and a degenerate Absalom." Against this pamphlet Brochmand delivered a series of lectures which after his death were collected and published under the title Apologiæ, speculi veritatis confutatio (Copenhagen, 1653). He was ordained bishop of Zealand in 1639, and during his long and fruitful activity in this office reorganized the Danish church service, especially by abolishing the Latin choir, and by introducing Wednesday services during Lent. His reputation as a dogmatist was established by his Universæ theologiæ systema (2 vols., 1633) in which he proved himself a bitter opponent, not only of the Roman Catholics, but also of the Reformed, whom he calls "enemies of God and of truth." He wrote several devotional works, of which his Sabbati sanctificatio for more than two centuries was a favorite collection of sermons with the Danish people.