We compute an analytic expression for the pressure of a weakly magnetizeddeconfined QCD matter within one-loop Hard-Thermal-Loop perturbation theory(HTLpt) at finite temperature and chemical potential. We also discuss themodification of QCD Debye mass of such matter for an arbitrary magnetic field.It is found to exhibit some interesting features depending upon the threedifferent scales, {it {i.e}}, the quark mass, temperature and the strength ofthe magnetic field. We also obtain an analytic expression for Debye mass in aweak field approximation. The various divergences appearing in the quark andgluon free energies are regulated through appropriate counter terms. The lowtemperature behaviour of the pressure is found to strongly depend on themagnetic field than that at high temperature. We also discuss the specificproblem with one-loop HTLpt associated with the over-counting of certain ordersin coupling.
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