We propose Graphene Klein tunnel transistors (GKTFET) as a way to enforce current saturation while maintaining large mobility for high speed radio frequency (RF) applications. The GKTFET consists of a sequence of angled graphene p-n junctions (GPNJs). Klein tunneling creates a collimation of electrons across each GPNJ, so that the lack of substantial overlap between transmission lobes across successive junctions creates a gate-tunable transport gap without significantly compromising the on-current. Electron scattering at the device edge tends to bleed parasitic states into the gap, but the resulting pseudogap is still sufficient to create a saturated output (I D -V D ) characteristic and a high output resistance. The modulated density of states generates a higher transconductance (g m ) and unity current gain cut-off frequency (f T ) than GFETs. More significantly the high output resistance makes the unity power gain cut-off frequency (f max ) of GKTFETs considerably larger than GFETs, making analog GKTFET potentially useful for RF electronics. Our estimation shows the f T /f max of a GKTFET with 1 μm channel reaches 33 GHz/17 GHz, and scale up to 350 GHz/53 GHz for 100 nm channel (assuming a single, scalable trapezoidal gate). The f max of a GKTFET is 10 times higher than a GFET with the same channel length.