Chances are you have a DER encoded key. To convert it you can (likely) do this
openssl rsa -inform der -in <yourfile> -outform pem -out output.pem
Please note that this will only work for unencrypted RSA private keys. If you have a DSA or EC (or PKCS8 formatted) key you'll need to change the command a bit, but you did not provide enough detail for me to narrow it down for you.
(There are also many other private key formats such as PVK, so if this still doesn't work please provide some more information)