You could try this "version" of an F chord:


E ||-1-|---|---|---|---|---|---|---|---|
B ||-1-|---|---|---|---|---|---|---|---|
G ||---|-2-|---|---|---|---|---|---|---|
D ||---|---|-4-|---|---|---|---|---|---|
A ||---|---|-3-|---|---|---|---|---|---|
x ||---|---|---|---|---|---|---|---|---|


I've suggested the finger placement. The only really tricky bit is covering the B and high E with your first finger. Mute the low E string. Another option is to leave the high E string open:


E ||---|---|---|---|---|---|---|---|---|
B ||-1-|---|---|---|---|---|---|---|---|
G ||---|-2-|---|---|---|---|---|---|---|
D ||---|---|-4-|---|---|---|---|---|---|
A ||---|---|-3-|---|---|---|---|---|---|
x ||---|---|---|---|---|---|---|---|---|


Chord Finder says its an Fmaj 7 chord... sounds nice!