The electronic band structure, lattice vibration frequencies, and optical and magnetic properties of EuB4O7 crystal with α-SrB4O7-type structure are calculated within the density functional method. It is found that this compound is a dielectric with a band gap of the order of 4 eV. It is found that the ground state of this crystal is the state with ferromagnetic ordering of Eu2+ spins. Exchange interaction constants are calculated; the ferromagnetic ordering temperature is estimated within the molecular field approximation (T c ≈ 1 K). The EuB4O7 compound is a magnetic pyroelectric and, hence, can exhibit magnetoelectric properties. The calculated polarization change during ferromagnetic ordering of this crystal is 3973 μC/m2.