By virtue of some fundamental concepts,analysis methods and research results about the theories of value distribution and normal family for meromorphic functions and based on Marty's criterion for normality,the Picad theorem of meromorphic functions with real zeros was discussed and it is proved: let d∈N⁺,f be a transcendental meromorphic function on the complex plane C,if there exists M≥0,so that for f,all zeros of f are real number,all of whose poles have multiplicity at least 3 and f(z)=0⇒|f'(z)|≤M|z^d|,then f'-z^d has infinite zeros.