  We comprehensively studied the magnetotransport properties of LaAgSb$_2$
under high pressure up to 4 GPa, which showed unique successive charge density
wave (CDW) transitions at $T_{CDW1}\sim 210$ K and $T_{CDW2}\sim 190$ K at
ambient pressure. With the application of pressure, both $T_{CDW1}$ and
$T_{CDW2}$ were suppressed and disappeared at the critical pressures of
$P_{CDW1}=3.0$--3.4 GPa and $P_{CDW2}=1.5$--1.9 GPa, respectively. At
$P_{CDW1}$, the Hall conductivity showed a step-like increase, which is
consistently understood by the emergence of two-dimensional hollow Fermi
surface at $P_{CDW1}$. We also observed a significant negative
magnetoresistance effect when the magnetic field and current were applied
parallel to the $c$ axis. Shubnikov--de Haas (SdH) oscillation measurements
under pressure directly showed the changes in the Fermi surface across the CDW
phase boundaries. In $P<P_{CDW2}$, three major oscillation components,
$\alpha$, $\beta$, and $\gamma$, were identified, whose frequencies were
increased by application of pressure. The increment rate of these frequencies
was considerably larger than that expected from the shrinkage of lattice
constant, indicating the unignorable band modification under pressure. In the
normal metallic phase above $P>P_{CDW1}$, we observed a single frequency of
$\sim 48$ T with a cyclotron effective mass of 0.066 $m_0$, whose cross section
in the reciprocal space corresponded to only 0.22\% of the first Brillouin
zone. Besides, we observed another oscillation component with frequency of
$\sim 9.2$ T, which is significantly enhanced in the limited pressure range of
$P_{CDW2}<P<P_{CDW1}$. The amplitude of this oscillation was anomalously
suppressed in the high-field and low-temperature region, which cannot be
explained by the conventional Lifshitz--Kosevich formula.
