We study almost para-contact Finsler connections on the total space of a vector bundle. In a vector bundle of Finsler space we define a Finsler connection compatible with almost para-contact Finsler structure $(J,\eta,\xi)$ if horizontal and vertical derivatives of all the three elements vanish. We give the family of all Finsler connections compatible with $(J,\eta,\xi)$ and some interesting special cases.