Abstract: In this paper, we present new semidefinite programming (SDP) relaxation schemes for 0-1 unconstrained polynomial programming (0-1UPP) problems. We first construct an SDP relaxation based on matrix cone decomposition and (piecewise) linear approximation for (0-1UPP).  It is shown that this SDP bound is tighter than the standard linear form (SLF). We then use Lagrangian dual and sum of squares (SOS) relaxation to obtain SDP relaxations which are equivalent to Lasserre's SDP relaxations for (0-1UPP). This provides a new way to derive Lasserre's hierarchy of SDP relaxations for (0-1UPP).