Logical positivism is an important Western philosophy with a central idea of verification; the doctrine that all knowledge about matters of fact stems from and relies on sensory experience and remains hypothetical. It accepts scientific inquiry and rejects metaphysics. But Popper called himself 'a tottering old metaphysician' ... so will you consider Popper a logical positivists?
Usually Karl Popper is credited with having contributed to the death of logical positivism, so no, I wouldn't say Karl Popper is a logical positivist.
That being said, many analytic philosophers after logical positivism still kept much of the attitude of positivism, such as logical analysis, defining ones terms, skepticism towards "grand" metaphysical programs, respect for science and empirical results, and so on, while rejecting the specific doctrines of logical positivism. See AJ Ayer's humorous comments in an interview with Bryan Magee for example. Ayer thinks "nearly all of it was false" yet it was true in spirit.
Here, he criticised psychologism, naturalism, inductivism, and logical positivism, and put forth his theory of potential falsifiability as the criterion demarcating science from non-science.
Logical positivism had a number of philosophical positions one of which might be understood as the only meaningful source of knowledge and truth was that which might be verified. In contradistinction to this Popper believed that the position wasn't tenable and that the important philosophical question is whether or not one could determine whther or not a question is scientific through falsifiability. The former position is one that declares only science can provide truth, whereas the latter position speaks not to truth, but to a definition of science. Popper's views on truth, thus, were more in line with the less radical claim that truth can come from many sources other than science.