We consider the nonlinear eigenvalue problem (NEP) originated from Bose-Einstein Condensation (BEC) (BEC-like NEP for short).We extend the shifted symmetric higher-order power method(SS-HOPM) proposed by Kolda and Mayo for symmetric tensor eigenvalue to BEC-like NEP.We have shown that given a proper shift term,the Algorithm SS-HOPM is convergent theorically and numerically.We also analyze the influence of data disturbance on eigenvalues theoretically and numerically.