The present invention provides a high selectivity epoxysilicone-cross-linked polyimide membrane comprising a polyimide polymer with hydroxyl functional groups cross-linked with epoxy functional groups on epoxysilicone polymer. The present invention also provides a process for separating at least one gas from a mixture of gases using the high selectivity epoxysilicone-cross-linked polyimide membrane. The process comprises providing the high selectivity epoxysilicone-cross-linked polyimide membrane which is permeable to the at least one gas; contacting the mixture on one side of the membrane to cause the at least one gas to permeate the membrane; and removing from the opposite side of the membrane a permeate gas composition comprising a portion of the at least one gas which permeated the high selectivity epoxysilicone-cross-linked polyimide membrane.