  In this work, we construct a new kind of rainbow functions, which has
generalized uncertainty principle parameter. Then, we investigate modified
thermodynamic quantities and phase transition of rainbow Schwarzschild black
hole by employing this new kind of rainbow functions. Our results demonstrate
that the rainbow gravity and generalized uncertainty principle have a great
effect on the picture of Hawking radiation. They prevent black holes from total
evaporation and cause a remnant. In addition, after analyzing the modified
local thermodynamic quantities, we find that the effect of rainbow gravity and
the generalized uncertainty principle lead to one first-order phase transition,
two second-order phase transitions, and two Hawking-Page-type phase transitions
in the thermodynamic system of rainbow Schwarzschild black hole.
