Random numbers are a fundamental ingredient in fields such as simulation, modelling and cryptography. Good random numbers should be independent and uniformly distributed. Moreover, for cryptographic applications they should also be unpredictable. A fundamental feature of quantum theory is that certain measurement outcomes are intrinsically random and unpredictable. These can be harnessed to provide unconditionally secure random numbers. We demonstrate a real-time self-testing source independent quantum random number generator (SI-QRNG) that uses squeezed light as source. We generate secure random numbers by measuring the quadratures of the electromagnetic field without making any assumptions on the source other than an energy bound; only the detection device is trusted. We use a homodyne detection to alternatively measure theQ andP conjugate quadratures of our source.P measurements allow us to estimate a bound on any classical or quantum side information that a malicious eavesdropper may detain. This bound gives the minimum number of secure bits we can extract from theQ measurement. We discuss the performance of different estimators for this bound. We operate this QRNG with a squeezed state source and we compare its performance with a thermal state source. This is the first demonstration of QRNG using squeezed state as well as the first implementation of real-time quadrature switching for a SI-QRNG.