Thread-safe concurrent FIFO queue in C++
You are guarding the state of one variable

std::queue&lt;unsigned char*&gt; _queue_;


So you only have one mutex.

pthread_mutex_t push_mutex;
pthread_mutex_t pop_mutex;


If you have two then push and pop can modify queue at the same time.

Make sure your mutex locking is exception safe by using RAII. Note all operations were you do start operation stop should be done by using RAII. This is the most important concept in C++ look it up.

Don't use pointers in C++. They do not convey ownership symantics (which means you don't know who should delete it (or when it should be deleted)). In this case use std::string it solves all the problems.

I see calls pthread_XXX_init but not the equivalent destroy.

Because you have not defined them the default copy constructor and assignment operator will be created. Since your object contains resources (mutext and conditional) you probably don't want the default behavior. Either define them or disable them.

C++11 has a better set of threading constructs use those rather than the C pthread library.