Thermal convection between two horizontal walls kept at small amplitude nonuniform temperatures of the form, $T_L=T_1+a{Delta}T$ sin kx and $T_U=T_2+b{Delta}T;sin(kx-{eta})$ with a, $b{ll}1$, is numerically investigated. When the Rayleigh number is small, an upright cell is formed between two walls at ${eta}=0$; the cell is tilted at ${eta}={pi}/2$, and a flow with two-tier-structure cells occurs at ${eta}={pi}$. As the Rayleigh number is increased, Nusselt number increases smoothly for ${eta}=0;and;{pi}/2$, but increases rather steeply for ${eta}={pi}$ near the critical Rayleigh number ($Ra_c=1708$). When the wave number is small (k=0.5), multicellular convection occurs over one wave length, for all phase differences, and multiple solutions are found.