It is known that an electric charge at rest has electric field in the region around it, but no magnetic field. A moving charge produces both the electric and magnetic fields.
If a charge is moving with a constant velocity, the electric and magnetic fields will not change with time, hence no EM wave will be produced.
But if the charge is moving with a non-zero acceleration, both the electric and magnetic field will change with space and time, it then produces EM wave. This shows that an accelerated charge emits electromagnetic waves.