Is ZF${}-{}$(Axiom of Infinity) consistent? Godel's theorem implies that Con(ZF) is not provable in ZF since it contains the axiom of infinity.
So is it consistent if the Axiom of infinity is removed?

Your question is unclear.
It is true that $\sf ZF$ cannot prove its own consistency. But $\sf ZF$ can prove the consistency of $\sf ZF-Infinity$, simply by verifying that the set of hereditarily finite sets satisfies all the axioms of $\sf ZF$ except the axiom of infinity.
This set, often denoted by $HF$ or $V_\omega$ can be defined as follows, $V_0=\varnothing, V_{n+1}=\mathcal P(V_n)$, and $V_\omega=\bigcup V_n$. Note that all the elements of $V_\omega$ are finite, and their elements are finite and so on.
On the other hand, if you want to ask whether or not $\sf ZF-Infinity$ proves its own consistency, then the answer is no. The reason is that this theory satisfies the requirements of the incompleteness theorem, and therefore cannot prove its own consistency (unless it is inconsistent to begin with).
