In laser direct-driven fusion, high power lasers are used to ablate the target shell, compress and heat the fuel with the spherical focusing rocket effect, to approach to the fusion ignition conditions. The shaped nanosecond laser pulses compress and accelerate the DT target symmetrically, and forms a high density plasma hot-spot at stagnation. The hydrodynamic instabilities, especially the Rayleigh-Taylor instability, which happens at the interface of plasmas, may destroy the compressed shells, and thus reduce the temperature and density of the hot-spot. In this paper is analyzed theoretically the hydrodynamic instability growth under the conditions in the 2020 winter experiment of the double-cone ignition scheme proposed by Zhang et al. (2020 Philos. Trans. A Math. Phys. Eng. Sci. 378 20200015). Both analytical model and one-dimensional simulations indicate that the fuel shells are compressed with low adiabat under the current quasi-isentropic waveform. The Rayleigh-Taylor instability remains in safe region with a maximum perturbation amplitude reaching 0.25 of the shell thickness at the most peak grown moment. The growth of the hydrodynamic instabilities can be further reduced by increasing the thickness of the shell, through using high foot pre-pulses and improving the uniformity of the target surface and laser irradiation in the future design.