When we write to any professor, we write Dear Professor X. If we write only Professor X, is it weird?
What you write is probably fine if you are in a place where it is proper to address the person as "professor". In some very formal places you might need to be more specific about titles, but in the US, for example, it would be fine, even if the person isn't, technically, a Professor, say an adjunct.
The "Dear" is superfluous and unneeded. But no one would likely object if you write it also.