The present invention relates to a process for producing an electrical steel sheet. In order to prevent aging deterioration of the electrical steel sheet, the carbon content of the steel for the sheet should be reduced to an extremely low level, e.g., 0.0030% or less. However, when molten steel was subjected to vacuum-degassing and continuous-casting procedures to prepare steel for a electrical steel sheet in a prior art, although a desired carbon content of the molten steel was ensured at the degassing stage, the carbon content of the steel sometimes exceeded the desired level at the slab range. In the present invention, the prior art problem is solved by carrying out the degassing procedure under conditions in which the ultimate degree of vacuum in the degassing vessel is 1.0 mmHg or less, the rate of inert gas blown per gas-blowing orifice is from 30 to 150 Nl/min, and the final carbon content of the molten steel is 0.0030% or less and by using means contacting the melt during the continuous-casting procedure, the carbon content of said means being 3.0% or less.