Abstract: Based on the previous paper, considering the non-uniformity in meridional direction and anomaly of sea surface temperature, the author continued to study the influence of water budget balance and moisture-convergence of boundary-layer on Madden-Julian oscillation. The results show that the influence on the propagating character of modified Kelvin and Rossby waves is not important, but for the instability. when the sea surface temperature anomaly is positive, the e-folding time for the amplification of the modified Kelvin wave reduced about 14.5%,the unstable growth increases with the characteristic scale of heating source, as the scale equals two times of Rossby deformation radius, the unstable growth reaches its maximum, when the scale continues to increase, the growth will reduce. When the sea surface temperature anomaly is negative, the e-folding time for the amplification of the modified Kelvin wave grows about 20%. the unstable growth reduces with the increase of the characteristic scale of cooling source, as the scale equals two times of Rossby deformation radius. the unstable growth reaches its minimum, when the scale continues to increase, the growth will increase, but it is always smaller than the case unconsidering the sea surface temperature anomaly. For the two modified Rossby waves, the wave with a smaller meridional scale decays except for extra-longwaves;another wave with a larger meridional scale grows in short-wave bands.