Yes, there is. See http://askubuntu.com/a/721387/196423 for details.
JabRef requires at least Java 8. Please follow the steps provided on our installation page.
You might see the error message
Error: Could not find or load main class net.sf.jabref.JabRefMain.
This means, you do not have JavaFX support activated in your Java runtime environment.
This typically happens if you use OpenJDK, where one needs to setup OpenJFX seperately.
You have several Java Virtual Machines installed, and under the command line the wrong one is chosen. Have a look at the previous question that tells you how to change the virtual machine used.
For Ubuntu you may also have a look at the Ubuntu page on Java.
As far as we know, JabRef is not yet running on these free JVMs, due of our dependencies. However, JabRef is reported to run nicely on the IcedTea runtime, which is based on the OpenJDK built with GNU Classpath to fill in missing classes. Some issues have been encountered with the look and feel (see issues #393 and #2003). Please let us know if newer versions give different results. If you have an idea or the expertise to make JabRef work under Classpath, let us know.