Yes, of course you can
For instance:
We have 2-SAT( http://en.wikipedia.org/wiki/2-satisfiability ), that is an problem in P.We we We have SATCNFSAT( http://en.wikipedia.org/wiki/Boolean_satisfiability_problem ) which is an NP-complete problem. We can convert all 2-sat instances to satcnfsat instances
If we have a 2-SAT formula like this:
$$ (x_{1} \vee x_{2}) \wedge (\neg x_{3} \vee x_{4}) $$
we can convert it to SATCNFSAT by inserting a dummy variable in each clause:
$$ (x_{1} \vee x_{2} \vee \neg x_{5}) \wedge (\neg x_{3} \vee x_{4} \vee \neg x_{6}) \wedge x_{5} \wedge x_{6} $$