The effect of annealing conditions of the cold-rolled strip made of a new aluminum–magnesium alloy 1565ch, containing zinc and zirconium, on the evolution of the grain structure has been analyzed in this work. This material was recently developed by Russian scientists and has already been used in transport engineering, but has not yet been sufficiently studied. Recrystallization processes occurring in this alloy and their connection with intermetallic particles are of particular interest. This work is aimed at studying the effect of the temperature and annealing time on the grain size in the 1565ch alloy. The grain structure has been studied by optical microscopy, and the intermetallic particles have been studied by scanning electron microscopy. In addition, the phase composition of the 1565ch alloy has been calculated using Thermo-Calc software. The grain size after achieving the recrystallization threshold has been shown to be insensitive to the annealing time and directly depends only on the annealing temperature, which no longer has a noticeable effect after 350°C. The 1565ch alloy tends to recrystallization with involving coarse intermetallic particles of the second phase. These particles are Al6(Mn, Fe) and Mg2Si. In addition, the effect of fine intermetallic particles on the recrystallization process has been investigated. The dissolution and coagulation of the fine particles in this alloy provoke rapid recrystallization.