The low-energy spin dynamics near the ferromagnetic quantum critical point in CePd 0.15 Rh 0.85 have been investigated using zero-field ͑ZF͒ and longitudinal-field muon spin relaxation ͑SR͒ measurements over a temperature range of 60 mK to 4 K and in applied fields up to 2500 G. The ZF-SR measurements reveal a considerable slowing down of the spin fluctuations with decreasing temperatures below 2 K. There is no clear sign of either static long-range magnetic ordering or spin freezing down to 60 mK. The temperature dependence of the ZF-muon depolarization rate ͑͒ exhibits a power-law behavior, ͑T͒ϳT −n with n ϳ 0.8, while the field dependence at 0.1 K reveals a time-field scaling of the muon relaxation function, P z ͑t , H͒ = P z ͑t / H ␥ ͒ with ␥ ϳ 1.0Ϯ 0.1. Furthermore, the exponent derived from the ZF-SR data agrees well with the power-law behavior of the temperature-dependent susceptibility, ͑T͒ϳT −␣ ͑␣ ϳ −0.6Ϯ 0.1͒, the E / T scaling of the neutron dynamical susceptibility, as well as the magnetization-field-temperature scaling ͑␥ m ϳ 0.8Ϯ 0.1͒, obtained from the same sample. The SR results of CePd 0.15 Rh 0.85 are discussed in the context of systems exhibiting non-Fermi-liquid behavior.