  Multiparameter quantum estimation theory aims to determine simultaneously the
ultimate precision of all parameters contained in the state of a given quantum
system. Determining this ultimate precision depends on the quantum Fisher
information matrix (QFIM) which is essential to obtaining the quantum
Cram\'er-Rao bound. This is the main motivation of this work which concerns the
computation of the analytical expression of the QFIM. Inspired by the results
reported in J. Phys. A 52, 035304 (2019), the general formalism of the
multiparameter quantum estimation theory of quantum Gaussian states in terms of
their first and second moments are given. We give the analytical formulas of
right logarithmic derivative (RLD) and symmetric logarithmic derivative (SLD)
operators. Then we derive the general expressions of the corresponding quantum
Fisher information matrices. We also derive an explicit expression of the
condition which ensures the saturation of the quantum Cram\'er-Rao bound in
estimating several parameters. Finally, we examine some examples to clarify the
use of our results
