A self-centered person is excessively concerned with himself and his own needs. He's selfish.

You probably know some people who always talk about themselves, make every issue about themselves, and are generally all about "Me, me, me!" People like that are self-centered: as the word suggests, they are overly centered on themselves. Self-centered people tend to ignore the needs of others and only do what's best for them. You can also call them egocentric, egoistic, and egoistical. In the seventeenth century, however, self-centered meant "fixed or stationary."

Definitions of self-centered

adj limited to or caring only about yourself and your own needs

egocentric, egoistic, egoistical, self-centred
self-absorbed, self-involved
absorbed in your own interests or thoughts etc
concerned chiefly or only with yourself and your advantage to the exclusion of others
altruistic, selfless
showing unselfish concern for the welfare of others
disregarding your own advantages and welfare over those of others
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