Using a cosmological

simulation, we analyze the differences between the widely-used spin parameters suggested by Peebles and Bullock. The dimensionless spin parameter

proposed by Peebles is theoretically well-justified but includes an annoying term, the potential energy, which cannot be directly obtained from observations and is computationally expensive to calculate in numerical simulations. The Bullock's spin parameter

avoids this problem assuming the isothermal density profile of a virialized halo in the Newtonian potential model. However, we find that there exists a substantial discrepancy between

and

depending on the adopted potential model (Newtonian or Plummer) to calculate the halo total energy and that their redshift evolutions differ to each other significantly. Therefore, we introduce a new spin parameter,

, which is simply designed to roughly recover the value of

but to use the same halo quantities as used in

. If the Plummer potential is adopted, the

is related to the Bullock's definition as

. Hence, the new spin parameter

distribution becomes consistent with a log-normal distribution frequently seen for the

while its mean value is much closer to that of

. On the other hand, in case of the Newtonian potential model, we obtain the relation of

; there is no significant difference at z = 0 as found by others but

becomes more overestimated than

or

at higher redshifts. We also investigate the dependence of halo spin parameters on halo mass and redshift. We clearly show that although the

for small-mass halos with

<

seems redshift independent after z = 1, all the spin parameters explored, on the whole, show a stronger correlation with the increasing halo mass at higher redshifts.