There is provided a method and apparatus for accessing a memory according to a processor instruction. The apparatus includes: a stack offset extractor extracting an offset value from a stack pointer offset indicating a local variable in the processor instruction; a local stack storage including a plurality of items, each of which is formed of an activation bit indicating whether each item is activated, an offset storing an offset value of a stack pointer, and an element storing a local variable value of the stack pointer; an offset comparator comparing the extracted offset value with an offset value of each item and determining whether an item corresponding to the extracted offset value is present in the local stack storage; and a stack access controller controlling a processor to access the local stack storage or a cache memory according to a determining result of the offset comparator.