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Let （X,T） be a topological dynamical system. A sequence F={fn}n=1∞of functions on X is called sub-additive if each fn is continuous non-negative valued function on X such thatu is an open cover of X, for any T-invariant measureμ, let F*（μ）=（?）fndμ. The topological pressure is defined for sub-additive potentials via open covers, then we set up a variational principleand the supremum can be attained by a T-invariant ergodic measure.where hμ（T,u） denotes the measure-theoretic entropy ofμ, relative to u. The main purpose of this paper is to generalize the result of Wen Huang and Yingfei Yi [8], in the paper [8], they proved the local variational principles of pressure for additive potentials .Furthermore, if F satisfies lim sup lim sup （?） logη?（T,ε）=0, whereηn（F,ε）=sup supwe prove the result P（T,F）=（?）P（T,F;u）.Then we have P（T,F）=（?） {hμ（T）+F*（μ）:μ∈M（X,T）}. another proof of topological pressure variational principle for sub-additive potentials [4] can be abtained.
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