The evolution of simulation and implementation of P systems has been intense since the theoretical model of computation was created. In the field of software simulation of P systems, the proposals made so far have taken advantage mainly of the parallelism of GPUs, but not of the parallelism of existing multi-core processors. This paper proposes a new model for simulating P systems using a multi-threaded approach in a multi-core processor. This simulation approach establishes a new paradigm that is entirely in line with the philosophy of P-systems: since objects must react in parallel, asynchronously and autonomously with other objects, simulation using multiple synchronized threads completely mimics the behavior of objects within a membrane. This proposal has been implemented and tested using a simulator programmed in C#, and its correct operation has been tested for confluent and non-confluent systems. The experimental results confirm that the simulator scales well with the number of hardware threads of a multiprocessor. The obtained results show that the new model is correct and that it can be extended to other more complex types of P systems, in order to discover which are the limit of this multi-threaded approach when running it in multi-core processors.