We propose a method to implement a quantum computer by solid-state NMR. We can use the J-coupling for the quantum gate in CdTe. Both Cd and Te have two isotopes with spin 1/2, then we can have 4-qubits. The decoherence by dipole interaction may be minimized by preparing the isotope superlattice grown in the order of—111Cd–123Te–113Cd–125Te—in the [111] direction and by applying the magnetic field in the direction of [100], the magic angle of the dipole interaction. The optical pumping technique can be used in CdTe to make the initialization of the qubits.