An Fe--Cr--Ni alloy for electron gun electrodes comprises: 15 to 20% Cr; 9 to 15% Ni; 0.12% or less C; 0.005 to 1.0% Si; 0.005% to 2.5% Mn; 0.03% or less P; 0.0003 to 0.0100% S; 2.0% or less Mo; 0.001 to 0.2 % Al; 0.003% or less O; 0.1% or less N; 0.1% or less Ti; 0.1% or less Nb; 0.1% or less V; 0.1% or less Zr; 0.05% or less Ca; 0.02% or less Mg; and the balance Fe and inevitable impurities by weight, and the alloy has a surface roughness satisfying the following formula in defining kurtosis in the rolling direction and kurtosis in the transverse direction to the rolling direction in surface roughness of the alloy as respectively Kr.sub.0 and Kr.sub.90 Kr.sub.0.ltoreq.4, Kr.sub.90.ltoreq.4